
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 the constant \\(a \in \mathbb{R}\\), and the function \\(f(x) = a\sin 2x + 2\cos^2 x\\).

\\(⑴\\) If \\(f(x)\\) is an even function, find the value of \\(a\\).

\\(⑵\\) If \\(f\left( \frac{\pi}{4}\right) =\sqrt{3}+1\\), find the solutions of the equation \\(f\left(x\right)=1- \sqrt{2} \\) in the interval \\(\left[-\pi,\pi\right] \\).

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