
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 $f\left( x \right)=\sin \left( 2x+\phi \right)\left(\left| \phi \right| < \dfrac{\pi }{2} \right)$ whose graph is symmetric about the point $\left( \dfrac{\pi }{3},0 \right)$, and $f\left( {{x}_{1}} \right)+f\left( {{x}_{2}} \right)=0$ when ${{x}_{1}},{{x}_{2}}\in \left( \dfrac{\pi }{12},\dfrac{7\pi }{12} \right)$ $\left( {{x}_{1}}\ne {{x}_{2}} \right)$, find $f\left( {{x}_{1}}+{{x}_{2}} \right)$.

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