Akt Inhibitor MK-2206 and Anastrozole With or Without Goserelin Acetate in Treating Patients With Stage II-III Breast Cancer

Inclusion Criteria: * Clinical T2-T4c, any N, M0 invasive ER+ (Allred score of 6-8) and HER2 negative (0 or 1+ by immunohistochemistry \[IHC\] or fluorescence in situ hybridization \[FISH\] negative for amplification) breast cancer, by American Joint Committee on Cancer (AJCC) 7th edition clinical staging, with the goal being surgery to completely excise the tumor in the breast and the lymph node; * Note: if the patient has invasive or ductal carcinoma in situ (DCIS) in the contralateral breast the patient is not eligible for this study * \>= 1 measurable lesion that is palpable, its size can be measured by bi-dimensional tape, ruler or caliper technique, and the minimum size of the largest tumor diameter is greater than 2.0 cm by imaging or physical examination * Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 * Life expectancy \> 4 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 100,000/mcL * Total bilirubin =\< upper limit of normal (ULN) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional ULN * Creatinine =\< ULN OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine above institutional normal * Patient with diabetes mellitus: fasting glucose =\< 120 mg/dL and hemoglobin A1c (HbA1c) =\< 8% * Negative serum pregnancy test =\< 7 days prior to pre-registration for women of childbearing potential * Ability to understand and the willingness to sign a written informed consent document * Patient is postmenopausal or premenopausal * NOTE: postmenopausal women, verified by * Bilateral surgical oophorectomy, or * No spontaneous menses \>= 1 year or * No menses for \< 1 year with follicle stimulating hormone (FSH) and estradiol levels in postmenopausal range, according to institutional standards or * Premenopausal women, verified by: * Regular menses or * FSH and estradiol levels in premenopausal range, according to institutional standards * Willingness to provide biologic samples for PIK3CA sequencing and correlative studies * Positive for PIK3CA mutation based on central laboratory testing * In premenopausal women, serum estradiol level in postmenopausal range =\< 7 days prior to registration Exclusion Criteria: * Any of the following for treatment of this cancer including: * Surgery * Radiation therapy * Chemotherapy * Biotherapy * Hormonal therapy * Investigational agent prior to study entry * Receiving any other investigational agents * History of allergic reactions attributed to compounds of similar chemical or biologic composition to MK-2206 or other agents used in this study * Prior axillary lymph node sampling (sentinel lymph node biopsy or axillary lymph node dissection); NOTE: fine needle aspiration (FNA) of axillary lymph node is acceptable * Invasive cancer or DCIS in the contralateral breast * Receiving any medications or substances that are strong inhibitors or inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP450 3A4); * NOTE: oxidative metabolism of MK-2206 in human liver microsomes is catalyzed primarily by CYP3A4, although direct glucuronidation also occurs; at least 7 days washout period is required in patients who were previously taking strong inhibitors or inducers of CYP.450 3A4; patients who are currently taking moderate inhibitors or inducers of CYP450 3A4 are encouraged to switch to other medications that do not interact with CYP450 3A4 * Corrected QT interval (QTc) prolongation (defined as a QTc interval \> 480 msec) or other significant electrocardiogram (ECG) abnormalities * Receiving any medications or substances with risk of torsades de pointes; Note: medications or substances on the list "Drugs with Risk of Torsades de Pointes" are prohibited; medications or substances on the list "Drugs with Possible or Conditional Risk of Torsades de Pointes" may be used while on study with extreme caution and careful monitoring * Uncontrolled intercurrent illness including, but not limited to: * Ongoing or active infection * Symptomatic congestive heart failure * Unstable angina pectoris * Uncontrolled symptomatic cardiac arrhythmia * Psychiatric illness/social situations that would limit compliance with study requirements * Any of the following: * Pregnant women * Nursing women * Women of childbearing potential who are unwilling to employ adequate contraception * NOTE: breastfeeding should be discontinued if the mother is treated with MK-2206; women of childbearing potential must use two forms of contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation * Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral therapy; NOTE: HIV-positive patients on combination antiretroviral therapy are ineligible; in addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy * Evidence of inflammatory cancer (clinical presentation of skin erythema involving more than one third of the breast or pathological evidence of dermal lymphatic involvement) * Patients with known metastatic disease are excluded * Current use of therapeutic anticoagulation therapy * Previous excisional biopsy of the breast cancer * Any condition (e.g., gastrointestinal tract disease resulting in an inability to take oral medication or a requirement for intravenous \[IV\] alimentation, prior surgical procedures affecting absorption) that impairs patients ability to swallow MK-2206 tablets