
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
After the curve C undergoes the scaling transformation $$\begin{cases} \left.\begin{matrix}x′= \frac {1}{2}x \\ y′=3y\end{matrix}\right.\end{cases}$$, the equation of the corresponding curve is: $x^{2}+y^{2}=1$. Derive the original equation of curve C.

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