
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 an origin-centered polar coordinate system where the positive half-axis of $x$ is the polar axis, and employing the same unit length in both the polar and Cartesian coordinate systems. The parametric equation of line $l$ is 
$$
\begin{cases} 
x=t+1\\
y=t-3
\end{cases}
$$
($t$ is the parameter), and the polar equation of circle $C$ is $\rho=4\cos \theta$. Find the length of the chord created by the intersection of line $l$ with circle $C$.

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