
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
Given the origin of the Cartesian coordinate system as the pole and the positive half-axis of \(x\) as the polar axis, establishing a polar coordinate system with the same unit length in both coordinate systems, find the length of the chord cut by the line \(l\) on the curve \(C\), where the parametric equation of line \(l\) is \(\begin{cases} & x=2+t \\ & y=1-t \\ \end{cases}\) and the polar equation of curve \(C\) is \(\rho=4\sin \theta\).

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