
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 acute triangle $ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Given vectors $\overrightarrow{m} = (2\sin(A + C), \sqrt{3})$ and $\overrightarrow{n} = (\cos 2B, 2\cos^2 \frac{B}{2} - 1)$, and vectors $\overrightarrow{m}$ and $\overrightarrow{n}$ are collinear.
(1) Find the measure of angle $B$;
(2) If $b = 1$, find the maximum value of the area $S_{\triangle ABC}$ of triangle $ABC$.

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