
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 sides opposite to angles \\(A\\), \\(B\\), and \\(C\\) are \\(a\\), \\(b\\), and \\(c\\) respectively, and it is given that \\(\dfrac{2b- \sqrt{3}c}{ \sqrt{3}a}= \dfrac{\cos C}{\cos A} \\).

\\((1)\\) Find the value of angle \\(A\\);  
   \\((2)\\) If angle \\(B= \dfrac{\pi}{6} \\) and the median to side \\(BC\\), \\(AM= \sqrt{7} \\), find the area of \\(\triangle ABC\\).

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