
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
Let \\(\triangle ABC\\) have internal angles \\(A\\), \\(B\\), and \\(C\\) opposite to sides of lengths \\(a\\), \\(b\\), and \\(c\\) respectively, and it satisfies \\(a^{2}+c^{2}-b^{2}= \sqrt {3}ac\\).  
\\((1)\\) Find the size of angle \\(B\\);  
\\((2)\\) If \\(2b\cos A= \sqrt {3}(c\cos A+a\cos C)\\), and the median \\(AM\\) on side \\(BC\\) has a length of \\(\sqrt {7}\\), find the area of \\(\triangle ABC\\).

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