
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 Cartesian coordinate system $xOy$, the parametric equation of line $l$ is given by 
$$
\begin{cases}
x = 3 + 3t \\
y = 1 - 4t
\end{cases}
(t \text{ is the parameter}),
$$
and the parametric equation of circle $C$ is given by 
$$
\begin{cases}
x = r \cos \theta \\
y = r \sin \theta
\end{cases}
(\theta \text{ is the parameter}, r > 0),
$$
If the chord cut by line $l$ on circle $C$ has a length of 4, find the value of $r$.

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