
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 an even function $f\left(x\right)$, for any $x$, $2f\left(x\right)+xf'\left(x\right) \gt 6$. Also, $f\left(1\right)=2$. The solution set of the inequality $x^{2}f\left(x\right) \gt 3x^{2}-1$ is ______.

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