
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 $f(x)=\ln({x}^{2}+1)$ and $g(x)={(\frac{1}{2})}^{x}-m$, if for $\forall x_{1}\in \left[0,3\right]$, $\forall x_{2}\in \left[1,2\right]$, $f(x_{1})\geqslant g(x_{2})$, then the range of real number $m$ is ______.

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