
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 rectangular coordinate system $xOy$, the parametric equations of line $l$ are given by: $\begin{cases} x=1+t \\ y=2-2t \end{cases}$ ($t$ is the parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive semi-axis of $x$ as the polar axis. The polar equation of circle $C$ is $\rho=2\cos\theta$. The line $l$ intersects the circle at points $A$ and $B$. Calculate the length of the segment $AB$.

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