
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 a polar coordinate system, the polar equation of curve C is $\rho=2\cos\theta+2\sin\theta$. Establish a Cartesian coordinate system with the pole as the origin and the positive x-axis as the polar axis. The parametric equation of line l is $\begin{cases} x=1+t \\ y= \sqrt{3}t \end{cases}$ (t is the parameter). Find the length of the chord that curve C cuts off on line l.

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