
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 that the solution set of the inequality $\frac{{2-x}}{{2x-1}} > 1$ is $A$, and the solution set of $x^{2}+2x+1-m\leqslant 0\left(m \gt 0\right)$ is $B$, if "$x\in A$" is a sufficient but not necessary condition for "$x\in B$", then the range of real number $m$ is ____.

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