
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) = 4cos(x)sin(x - π/6) + 1,
(I) Find the interval(s) where f(x) is monotonically increasing;
(II) Find the maximum and minimum values of f(x) in the interval [-π/12, 5π/12].

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