
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 $f\left(x\right)=(m^{2}+3m-9)x^{m-1}$ is a decreasing function on $\left(0,+\infty \right)$, where $m\in R$.  
$(1)$ Find the analytical expression of $f\left(x\right)$;  
$(2)$ If ${({2-a})^{\frac{1}{{m-1}}}}>{({2a-1})^{\frac{1}{{m-1}}}}$, find the range of real number $a$.

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