
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
Translate the graph of the function $f(x)=3\sin (\frac{x}{2}+\frac{\pi }{3})$ by shifting it $\frac{\pi }{3}$ units to the right, then stretch the horizontal coordinates of all points on the graph to twice their original length (while keeping the vertical coordinates unchanged) to obtain the graph of $y=g(x)$. Determine the analytical expression for $y=g(x)$.

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