
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 $f(x)=\sqrt{2}\sin(2x+\phi), (-\pi < \phi < 0)$, 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 $\phi$.
2. Determine the interval(s) where $f(x)$ is strictly decreasing.
3. Find the range of $f(x)$ on the interval $\left[0, \frac{\pi}{2}\right]$.

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