
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 $f\left(x\right)=(m^{2}-m-1)x^{m}$ defined on $R$.  
$(1)$ Find the analytical expression of the function $f\left(x\right)$;  
$(2)$ Solve the inequality with respect to $x$: $f\left(x\right) \gt \left(k+2\right)x-2k\left(k\in R\right)$.

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