
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 $f(x) = 2\sin^2x - \sin\left(2x - \frac{5\pi}{6}\right)$, where $x \in \mathbb{R}$.

(I) Find the maximum value of the function $f(x)$, and write the set of values of $x$ when $f(x)$ reaches its maximum value.

(II) If the acute angle $\theta$ satisfies $\tan\theta = 2\sqrt{2}$, find the value of $f(\theta)$.

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