Patients with a history of toxic epidermal necrolysis (TEN) or Stevens-Johnson syndrome are excluded Patients with Down syndrome Patients with a motor, visual, or auditory handicap that prevents computer use (e.g., unresolved posterior fossa syndrome) are not eligible to participate in this trial Patients must not have POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes) Sinusoidal obstruction syndrome (SOS) if present, must be stable or improving clinically Active or a history of Tourettes syndrome or tic disorder Patients must not have been diagnosed with myelodysplastic syndrome or with any malignancy other than neuroblastoma Malabsorption syndrome or other conditions that would interfere with intestinal absorption No history of Stevens Johnsons syndrome, toxic epidermal necrolysis (TEN)s syndrome, or motor neuropathy RANDOMIZED PHASE II (ARMS K AND L): No history of Stevens Johnsons syndrome, TENs syndrome, or motor neuropathy Patients must not have evidence or history of veno-occlusive disease or sinusoidal obstruction syndrome Patients with Down syndrome are not eligible No known history of prolonged QT syndrome Patients known to have one of the following concomitant genetic syndromes: Down syndrome, Bloom syndrome, ataxia-telangiectasia, Fanconi anemia, Kostmann syndrome, Shwachman syndrome or any other known bone marrow failure syndrome Plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein (M-protein), and skin changes (POEMS) syndrome Diagnosis of Down syndrome (Trisomy 21) History of hospitalization in past 12 months for diabetic ketoacidosis (DKA) or hyperosmolar hyperglycemic nonketotic syndrome (HHNS) Patients must have constitutional trisomy 21 (Down syndrome) or trisomy 21 mosaicism (by karyotype or fluorescence in situ hybridization [FISH]) Malabsorption syndrome or other conditions that would interfere with intestinal absorption Have a confirmed diagnosis of sleep apnea or restless leg syndrome Abnormalities of the cornea based on history (e.g., dry eye syndrome, Sjogrens syndrome), congenital abnormality (e.g., Fuchs dystrophy), abnormal slit-lamp examination using a vital dye (e.g., fluorescein, Bengal Rose), and/or an abnormal corneal sensitivity test (Schirmer test or similar tear production test) Participants with persistently low CD4 counts less than 200 and a history of any acquired immune deficiency syndrome (AIDS)-defining infection in the last 6 months before screening are excluded from the study Patients with known diagnoses that are associated with germline DDR defects such as Li Fraumeni syndrome and ataxia telangiectasia are excluded from the study Patients with any of the following diagnoses:* Acute promyelocytic leukemia (APL)* Down syndrome* Fanconi anemia, Kostmann syndrome, Shwachman syndrome or any other known bone marrow failure syndrome* Wilson's disease and any other disorder of copper metabolism* Juvenile myelomonocytic leukemia (JMML) Patients with Li Fraumeni syndrome are excluded from the study Patients must not have known Gilberts syndrome Significant conduction defects (i.e. second or third degree atrio-ventricular block or sick sinus syndrome) No known Gilberts syndrome or known homozygosity for UGAT1A1*28 polymorphism Patients with Down syndrome Patients with a history of myelodysplastic syndrome (MDS) Patients who are known to have Lynch syndrome and have been found to carry a specific germline mutation in an MMR gene (MLH1, MSH2, MSH6, PMS2) are eligible to participate Patient with and without Down syndrome are eligible and must have one of the following:* Second or greater relapse;* Primary refractory disease with at least 2 prior induction attempts;* First relapse refractory to at least one prior re-induction attempt* Any relapse after HSCT* First relapse with no prior re-induction attempt in setting of Down syndrome* Note: Patients with Down syndrome are eligible with any disease status including first relapse with no prior re-induction attempt; patients without Down syndrome are NOT eligible if in first relapse with no prior re-induction attempt Patients known to have one of the following concomitant genetic syndromes: Bloom syndrome, ataxia-telangiectasia, Fanconi anemia, Kostmann syndrome, Shwachman syndrome, or any other known bone marrow failure syndrome Down syndrome Patients with down syndrome are excluded from this study Patients with known symptomatic Fanconi anemia (FA), ataxia-telangiectasia (A-T) syndrome, Bloom syndrome (BS) and Nijmegen breakage syndrome (NBS) are not eligible (asymptomatic carriers are acceptable)