
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 parametric equation of line $l$ is 
$$
\begin{cases}
x = 1 + 2t \\
y = 1 - 2t
\end{cases} \quad (t \text{ is the parameter}),
$$
and the circle $C$ is given by
$$
\begin{cases}
x = 2\cos \alpha \\
y = 2\sin \alpha
\end{cases} \quad (\alpha \text{ is the parameter}).
$$
(I) Set up a polar coordinate system with the origin as the pole and the positive x-axis as the polar axis, and find the polar equation of circle $C$.
(II) Line $l$ intersects circle $C$ at points $A$ and $B$. Find the length of the chord $AB$.

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