
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 that $f(x) = 2\sin(2x + \frac{\pi}{6}) + a\cos 2x$ ($a \in \mathbb{R}$), and the graph of the function is symmetric about $x = \frac{\pi}{3}$.
(I) Find the analytic expression of function $f(x)$;
(II) When $\alpha \in (0, \frac{\pi}{3})$, and $f(\alpha) = \frac{6}{5}$, find the value of $\sin 2\alpha$.

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