
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 acute \\(\triangle ABC\\), the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are \\(a\\), \\(b\\), and \\(c\\) respectively, and it is given that \\( \sqrt {3}\cos A+\sin 2(B+C)=0\\).  
\\((1)\\) Find the value of \\(A\\);  
\\((2)\\) If \\(|b-c|= \sqrt {5}\\) and the area of \\(\triangle ABC\\) is \\( \sqrt {3}\\), find the value of \\(a\\).

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