
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 $y=\sin(2x+ \frac{\pi}{6})$, shrink the x-coordinates of each point on the graph to half of its original size (keeping the y-coordinates unchanged), and then shift the graph to the right by $\frac{\pi}{3}$ units to obtain the function $y=g(x)$. Calculate the value of $g(\frac{\pi}{3})$.

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