
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 $f\left( x \right)=2\sin \left( \omega x+\varphi \right)\left( \omega > 1,\left| \varphi \right| < \dfrac{\pi }{2} \right)$, its graph passes through the point $\left(0, \sqrt{3}\right)$, is monotonous on $\left( \dfrac{\pi}{12}, \dfrac{\pi}{3}\right)$, and after shifting the graph of $f\left( x \right)$ to the left by $\pi$ units, the resulting function graph is symmetric to the original function $f\left( x \right)$'s graph with respect to the $x$-axis. When $x_1,x_2\in\left(- \dfrac{7\pi}{18},- \dfrac{\pi}{9}\right),x_1\neq x_2 $, $f\left({x}_{1}\right)=f\left({x}_{2}\right) $, find $f\left({x}_{1}+{x}_{2}\right) =$\_\_\_\_\_\_\_\_\_\_\_\_．

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