
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 opposite to the angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is given that $b^2 = a^2 + c^2 + ac$.
1. Find the measure of angle $B$.
2. If $b = \sqrt{3}$ and $S$ is the area of triangle $ABC$, find the maximum value of $S + \sqrt{3}\cos A \cos C$ and the measure of angle $A$.

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