
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) = 2cos^2(x) - 2$\sqrt{3}$sin(x)cos(x).
(I) Find the monotonically decreasing interval of the function f(x);
(II) Find the sum of all the real roots of the equation f(x) = $- \frac{1}{3}$ in the interval [0, $\frac{\pi}{2}$].

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