
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 $f(x)=\sqrt{2}\sin(2x+\phi)$, where $|\phi|<\frac{\pi}{2}$, its graph is symmetric about the line $x=\frac{\pi}{12}$. When $x_1, x_2 \in \left(-\frac{17\pi}{12}, -\frac{2\pi}{3}\right)$ and $x_1 \neq x_2$, $f(x_1)=f(x_2)$. Determine the value of $f(x_1+x_2)$.

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