
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 $$f(x)= \begin{cases} \overset{-2,x>0}{x^{2}+bx+c,x\leq 0}\end{cases}$$, if $f(-4)=f(0)$ and $f(-2)=0$, find the solution set of the inequality $f(x) \leq 1$.

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