
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 a triangle $ABC$ with interior angles $A$, $B$, and $C$ opposite to sides $a$, $b$, and $c$ respectively, and it satisfies the equation $\frac{\sqrt{3} c}{\cos C} = \frac{a}{\cos\left(\frac{3\pi}{2}+A\right)}$.
(I) Find the value of $C$;
(II) If $\frac{c}{a} = 2$ and $b = 4\sqrt{3}$, calculate the area of $\triangle ABC$.

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