
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 a function $f\left(x\right)=\left\{\begin{array}{l}{-{x}^{2}-2x, x\leq m}\\{-x+2, x>m}\end{array}\right.$, if there exists a real number $x_{0}$ such that $f\left(x\right)\leq f(x_{0})$ holds for any real number $x$, then the range of real number $m$ is ______.

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