
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 odd function $f(x)$, which has a derivative $f''(x)$ on $\mathbb{R}$ and satisfies $f''(x) < x^2$ on $(0,+\infty)$, determine the range of the real number $m$ for which $f(1-m)-f(m) \geqslant \frac{1}{3}\left[ (1-m)^3 - m^3 \right]$.

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