
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the inequality system about $x$: $\left\{\begin{array}{l}{x>-1}\\{x\leq 1-k}\end{array}\right.$  
$(1)$ When $k=-2$, find the solution set of the inequality system.  
$(2)$ If the solution set of the inequality system is $-1 < x \leq 4$, find the value of $k$.  
$(3)$ If the inequality system has three integer solutions, then the range of $k$ is ______.

Present the answer in LaTex format: \boxed{Your answer}
user