
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 that the function $f(x)$ defined on $\mathbb{R}$ is an odd function, its derivative is $f′(x)$, and for any positive real number $x$, it satisfies $xf′(x) > 2f(-x)$. If $g(x)=x^{2}f(x)$, determine the solution set of the inequality $g(x) < g(1-3x)$.

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