
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 function $f\left(x\right)=(2m^{2}-m)x^{2m+3}$ is a power function, and the graph of the function $f\left(x\right)$ is symmetric about the $y$-axis.  
$(1)$ Find the value of the real number $m$;  
$(2)$ If the inequality $\left(a-1\right)^{m} \lt \left(2a-3\right)^{m}$ holds, find the range of real numbers for $a$.

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