
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
The function $f(x)=-x^{3}-2x^{2}+4x$ is defined on the interval $[-3,3]$. The inequality $f(x)\geqslant m^{2}-14m$ holds for all $x$ in this interval. Determine the range of possible values for the real number $m$.

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