
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 x-axis as the polar axis, establish a polar coordinate system with the same unit of length as in the Cartesian coordinate system. It is known that the parametric equation of line $l$ is $$\begin{cases} x=t+1 \\ y=t-2 \end{cases}$$ (where $t$ is the parameter), and the polar equation of circle $C$ is $\rho=4\cos\theta$.  
(1) Find the standard equations of line $l$ and circle $C$.  
(2) Find the length of the chord cut off by circle $C$ on line $l$.

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