
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 the power function $f\left(x\right)=x^{m-3}(m\in N^{*})$ is symmetric about the $y$-axis, and $f\left(x\right)$ is decreasing on $\left(0,+\infty \right)$, find the range of real numbers $a$ that satisfy $f\left(a+1-m\right) \lt f\left(3-2a-m\right)$______.

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