
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
Transform the graph of $y=f(x)$ by keeping the y-coordinate of each point unchanged and changing the x-coordinate to half of its original value. Then, reflect the graph along the x-axis to the left by $\frac{\pi}{6}$ units. If the resulting curve is the same as the graph of $y=\sin(2x)$, determine the expression for $f(x)$.

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