
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 the function $f(x)= \sin (2x + \varphi)+ a\cos (2x + \varphi)(0 < \varphi < \pi)$ has a maximum value of $2$, and satisfies $f(x)= f\left( \frac{\pi}{2}- x\right)$, find the possible values of $\varphi$.

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