
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 $f(x) = (m^3 - m + 1)x^{\frac{1}{2}(1-8m-m^2)}$ ($m \in \mathbb{Z}$), its graph does not intersect with the x-axis or the y-axis, and it is symmetric about the y-axis.

(1) Find the explicit formula of $f(x)$;  
(2) Solve the inequality $f(x+1) > f(x-2)$.

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