
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 $f(x) = \begin{cases} -(x-a)^2, & x\geq 0 \\ -x^2-2x-3+a, & x<0 \end{cases}$, if $f(x) \leq f(0)$ holds true for all $x \in \mathbb{R}$, then the range of $a$ is $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$.

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