
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
(Matrix and Transformation)  
Given matrices $$M= \begin{pmatrix} 1 & 0 \\ 0 & 2 \end{pmatrix}, N= \begin{pmatrix} \frac {1}{2} & 0 \\ 0 & 1 \end{pmatrix}$$, the transformation corresponding to the matrix product MN transforms the curve $y=\sin x$ into curve C. Find the equation of curve C.

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