
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
1. The cartesian equation of curve C is $x^2+y^2-2x=0$. Establish a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis. Find the polar equation of curve C.
2. Given the stretching transformation $$
\begin{cases}
x′=2x \\
y′= \frac {1}{3}y
\end{cases}
$$, curve C is transformed into an ellipse that satisfies $\frac {x′^{2}}{2}+y′^2=1$. Determine the equation of curve C.

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