
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)=(2m^{2}-2m-3)x^{2}$ is monotonically decreasing on $\left(0,+\infty \right)$.  
$(1)$ Find the value of $f\left(8\right)$;  
$(2)$ Solve the inequality: $f(x^{2}+2x) \lt f\left(x+6\right)$.

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