
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
In the Cartesian coordinate system xOy, the parametric equations of a circle are 
$$
\begin{cases}
x = 2 + 2\cos\alpha \\
y = 2\sin\alpha
\end{cases}
$$
($\alpha$ is the parameter). Taking the origin O as the pole and the positive x-axis as the polar axis, establish a polar coordinate system. Find:
(1) the Cartesian equation of the circle;
(2) the polar equation of the circle.

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