
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 $f(x)=2\sin (2x+\dfrac{\mathrm{ }\!\!\!\pi\!\!\!{ }}{6})$, if its graph is translated to the right by $\dfrac{\mathrm{ }\!\!\!\pi\!\!\!{ }}{6}$ units, resulting in the graph of function $g(x)$, find the equation of one symmetry axis of the graph of function $g(x)$.

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