
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
Define the operation $$a*b= \begin{cases} \overset{a(a\leq b)}{b(a>b)}\end{cases}$$．For example, 1\*2=1. Then, the intervals of monotonic increase for the function $f(x)=2\sin x*\cos x$ in the interval $[0, 2\pi]$ are \_\_\_\_\_\_ .

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