
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 has a line of symmetry at $x= \frac {\pi}{8}$ and $f(0) < 0$,  
$(1)$ find $\varphi$;  
$(2)$ find the intervals where $f(x)$ is monotonically decreasing;  
$(3)$ find the range of $f(x)$ on $\left[0, \frac {\pi}{2}\right]$.

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