
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 \( \Delta ABC \), the sides opposite angles A, B, and C are denoted as a, b, and c, respectively. It is given that \( ( \sqrt {3}\sin B-\cos B)( \sqrt {3}\sin C-\cos C) = 4\cos B\cos C \).
(1) Determine the measure of angle A;
(2) If a=2, find the range of the area of \( \Delta ABC \);
(3) If \( \sin B = p\sin C \), determine the range of the real number p such that \( \Delta ABC \) is an acute triangle.

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