
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 $ABC$, the sides $a, b, c$ are opposite to angles $A, B, C$ respectively, and satisfy the equation $b\cos C = (2a + c) \cos (\pi - B)$.

(1) Find the measure of angle $B$;
(2) If $b = \sqrt{13}$ and $S_{\triangle ABC} = \frac{3\sqrt{3}}{4}$, find $a + c$.

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