
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
Given the function f(x) = (sinx + $\sqrt{3}$cosx)(cosx - $\sqrt{3}$sinx),
1. Find the interval where the function f(x) is monotonically increasing.
2. If f(x0) = $\frac{6}{5}$, and x0 $\in$ [0, $\frac{\pi}{2}$], find the value of cos2x0.

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