
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 function $f\left(x\right)=\min \{-x^{2}$,$x-2\}$, where $\min \{a,b\}$ represents the minimum value between $a$ and $b$.  
$(1)$ Find the values of $f\left(0\right)$ and $f\left(4\right)$.  
$(2)$ Find the solution set for $f\left(x\right) \gt -4$.

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