
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 $f(x) = \sqrt{3}\sin{x}\cos{x} - \cos^2{x} - \frac{1}{2}$, where $x \in \mathbb{R}$. <br /> (I) When $x \in [-\frac{\pi}{12}, \frac{5\pi}{12}]$, find the values of $x$ at which the function $f(x)$ attains its maximum and minimum values. <br /> (II) Let $\triangle ABC$ have sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively, with $a = 2\sqrt{3}$, $b = 6$, and $f(\frac{A}{2}) = -1$. Find the value of $c$.

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