
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\\), \\(a\\), \\(b\\), and \\(c\\) are the sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) respectively, and it is given that \\(\sqrt{3}\sin C-\cos B=\cos (A-C)\\).

\\((1)\\) Find the measure of angle \\(A\\).

\\((2)\\) If \\(a=2\sqrt{3}\\) and the area of \\(\triangle ABC\\) is \\(3\sqrt{3}\\), find the values of \\(b\\) and \\(c\\).

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