Idle doesn't means "Doing nothing" in case of UE. UE used to be the most busiest during Idle mode and perform below operation:
In short, Idle Mode Procedure is the collective name of all the procedure which are happening during power-on and 'after power-on'. Major procedures for the idle mode can be described as follows :
i) Cell Measurement (Measure the signal quality of Neigbour cells)
ii) Cell Search/PLMN Search (Detect PLMN of cells and determine which cell it would camp on to)
iii) Cell Selection (Determine a cell and perform registration)
iv) Cell Reselection (Change cell from existing cells to another cell)
UE peforms the measurement for serving cell at every DRX cycle and check if it satisfy the cell selection criteria. If it successfully finds a cell meeting the criteria within a certain amount of trial, it stays at the cell but if it does not find the serving cell within a certain amount of trials (see the table shown below), it should initiate the measurement/evaluation for all the neighbour cells which is specified by the serving cell system information.