
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 $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ of $\triangle ABC$ respectively, and $\frac{\sqrt{3} a}{c} = \frac{\cos A + 2}{\sin C}$.
(I) Find the measure of angle $A$;
(II) If $b + c = 5$, and the area of $\triangle ABC$ is $\sqrt{3}$, find the value of $a$.

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