
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
Given a triangle \\(ABC\\), with sides \\(a\\), \\(b\\), and \\(c\\) opposite to angles \\(A\\), \\(B\\), and \\(C\\) respectively, and given \\(a=2b\cos C\\) and \\(\sin \left(A - \frac{\pi}{4}\right) + \sin B = \cos \left(\frac{\pi}{2} - C\right)\\):
- Find the measure of angle \\(A\\).
- If \\(a=2\\), find the area of triangle \\(ABC\\).

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