
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
(1) Given the power function $f(x) = (-2m^2+m+2)x^{-2m+1}$ is an even function, find the expression for $f(x)$;  
(2) Given $x+x^{-1}=3$ ($x>1$), find the value of $x^2-x^{-2}$.

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