
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 $f(x) = 2\sin(\omega x + \varphi)$ where $\omega > 0$ and $0 < \varphi < \pi$, is an even function, and the distance between two adjacent axes of symmetry of its graph is $\frac{\pi}{2}$:  
(1) Calculate the value of $f\left(\frac{\pi}{8}\right)$.  
(2) Determine the intervals where $f(x)$ is monotonically decreasing.

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