
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
Given that $a$, $b$, $c$ are the sides opposite to angles $A$, $B$, $C$ in $\triangle ABC$ respectively, and it satisfies $(a+b+c)(\sin B+\sin C-\sin A)=b\sin C$.

(Ⅰ) Solve for the magnitude of angle $A$;  
(Ⅱ) Given that $a=\sqrt{3}$, let $S$ be the area of $\triangle ABC$, find the maximum value of $S+\sqrt{3}\cos B\cos C$.

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