
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
In $\triangle ABC$, let the sides opposite to angles $A$, $B$, $C$ be $a$, $b$, $c$ respectively, and $a\cos C + \frac{1}{2}c = b$.
(1) Find the measure of angle $A$;
(2) If $a = \sqrt{15}$ and $b = 4$, find the length of side $c$.

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