
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 $f(x)=(m^{3}-m+1)x^{\frac {1}{2}(1-8m-m^{2})}$ ($m\in\mathbb{Z}$) whose graph has no intersection with the $x$-axis and $y$-axis and is symmetric about the $y$-axis.
(1) Find the analytic expression 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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