
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 function $y=\sin\left(2x+\frac{\pi}{6}\right)$ is transformed such that the horizontal coordinates of each point on the graph are reduced to $\frac{1}{2}$ of their original values, and then the graph is shifted to the right by $\frac{\pi}{3}$ units. Find the value of $g\left(\frac{\pi}{3}\right)$, where $g(x)$ is the resulting function.

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