
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 graph of the function $y=\sin x$ is translated three units to the right to obtain graph $C$. Then, all the abscissas of the points on graph $C$ are changed to $\frac{1}{2}$ of the original values (the ordinates remain unchanged) to obtain graph $C_{1}$. Determine the analytical expression of $C_{1}$.

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