
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 $y=\sin(2x+\frac{\pi}{3})$, after shifting the graph of the function to the right by $\frac{\pi}{6}$ units and doubling the y-values (keeping x-values constant), find the analytical expression of the resulting function.

A) $y=2\cos 2x$
B) $y=2\cos 2x$
C) $y=\frac{1}{2}\sin 2x$
D) $y=2\sin 2x$

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