
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
If $f(x)=\frac {1}{12}x^{4}- \frac {1}{6}mx^{3}- \frac {3}{2}x^{2}$, when $|m|\leqslant 2$ is a convex function on the interval $(a,b)$, find the maximum value of $b-a$.

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