
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 $xOy$, given a circle $C$: 
$$
\begin{cases}
x=5\cos \theta-1 \\
y=5\sin \theta+2
\end{cases}
(\theta \text{ is a parameter})
$$
and a line $l$: 
$$
\begin{cases}
x=4t+6 \\
y=-3t-2
\end{cases}
(t \text{ is a parameter})
$$
then the length of the chord formed by the intersection of line $l$ and circle $C$ equals \_\_\_\_\_\_.

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