
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
Let $f'(x)$ and $g'(x)$ be the derivative functions of $f(x)$ and $g(x)$, respectively. If $f'(x) \cdot g'(x) \leqslant 0$ always holds in interval $I$, then the monotonicity of functions $f(x)$ and $g(x)$ is said to be opposite in interval $I$. If the function $f(x)= \frac {1}{3}x^{3}-3ax$ and the function $g(x)=x^{2}+bx$ have opposite monotonicity in the open interval $(a,b)$ $(a > 0)$, then the maximum value of $b-a$ is \_\_\_\_\_\_.

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