
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 lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, and ${a}^{2}={b}^{2}+{c}^{2}+\sqrt{3}ab$.

(I) Find angle $A$.

(II) Let $a=\sqrt{3}$, and let $S$ be the area of $\triangle ABC$. Find the maximum value of $S+3\cos B\cos C$, and determine the value of $B$ in this case.

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