
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\\), \\(A\\), \\(B\\), and \\(C\\) are the three interior angles, and \\(a\\), \\(b\\), \\(c\\) are the sides opposite these angles, respectively. It is known that \\(b^{2}\\), \\(a^{2}\\), \\(c^{2}\\) form an arithmetic sequence.

\\((1)\\) Find the minimum value of \\(\cos A\\);

\\((2)\\) If \\(a=2\\), when \\(A\\) is at its maximum, what is the maximum area of \\(\triangle ABC\\)?

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