
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 $f(x)=2\sin (\omega x+\varphi)$ ($\omega > 0$, $|\varphi| < \frac{\pi}{2}$), 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}
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