
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 $f(x) = 2\sin(\omega x + \varphi)$ ($\omega > 0$, $|\varphi| < \frac{\pi}{2}$) passes through point B(0, -1), and is monotonic in the interval $\left(\frac{\pi}{18}, \frac{\pi}{3}\right)$, the graph of $f(x)$ coincides with its original graph after being shifted left by $\pi$ units. When $x_1, x_2 \in \left(-\frac{17\pi}{12}, -\frac{2\pi}{3}\right)$, and $x_1 \neq x_2$, determine the value of $f(x_1 + x_2)$ if $f(x_1) = f(x_2)$.

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