
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 $f(x)=\sqrt{2}\sin(2x+\varphi) (-\pi < \varphi < 0)$, the graph of the function has a symmetry axis along the line $x=\frac{\pi}{8}$ and $f(0) < 0$.

(1) Find the value of $\varphi$.
(2) Find the interval where $f(x)$ is monotonically decreasing.
(3) Find the range of $f(x)$ on the interval $[0, \frac{\pi}{2}]$.

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