
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 function $f(x)= \begin{cases} \frac{3(1-{2}^{x})}{{2}^{x}+1}, & (-1\leqslant x\leqslant 1) \\ - \frac{1}{4}({x}^{3}+3x), & (x < -1 \text{ or } x > 1) \end{cases}$, determine the range of values for $x$ such that $f(mx-1)+f(x) > 0$ holds true for any $m\in[-3,2]$.

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