CHICAGO — Cook County prosecutors will soon begin arguing in court that certain longtime inmates deserve more lenient sentences, State’s Attorney Kim Foxx’s office said Friday. Three men are slated for possible resentencing next week, the first to potentially benefit from a new state law allowing prosecutors to petition for shorter sentences ”if the original sentence no longer advances the interests of justice.” “The impact of injustice on these individuals, by actors including prosecutors, deserves to be remedied,” Foxx said in a statement. “Through the Resentencing Initiative, prosecutors ca…