
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 $f(x)$ defined on $\mathbb{R}$ with its derivative $f'(x)$, if $f(x)=f(2-x)$, and when $x > 1$, $f'(x) < 0$, then the range of real numbers $m$ that satisfy the inequality $f(m+1) \leqslant f(2m)$ is.

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