
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 the function $y=\sin x$ ($x \in \mathbb{R}$) by shrinking all the x-coordinates to half of their original values (keeping the y-coordinates unchanged), and then shifting all points of the graph to the left by $\dfrac{\pi}{6}$ units. Find the function represented by the resulting graph.

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