
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 $f(x)=\sin(2x-\frac{\pi}{6})-\cos(2x)$ $(x \in \mathbb{R})$.

(I) Find the smallest positive period, the maximum value of the function $f(x)$, and the set of $x$ when the maximum value is attained;

(II) Let $\triangle ABC$ be a triangle with sides opposite to angles $A$, $B$, and $C$ being $a$, $b$, and $c$ respectively. If $f\left(\frac{B}{2}\right) = -\frac{\sqrt{3}}{2}$, $b = 1$, $c = \sqrt{3}$, and $a > b$, find the angles $B$ and $C$.

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