
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
The graph of the function $f(x)=\sin \left(\omega x+{\frac {\pi }{3}}\right)\quad (\omega >0)$ has a distance between adjacent symmetry axes of ${\frac {\pi }{2}}$. If the graph of function $f(x)$ is shifted to the right by ${\frac {\pi }{6}}$ units, find the analytical expression of the new function $g(x)$.

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