
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
With the origin of the Cartesian coordinate system as the pole and the positive half of the $x$-axis as the polar axis, using the same unit of length in both coordinate systems, it is known that the polar equation of line $l$ is $\rho \sin (\theta - \frac{\pi}{3}) = 6$, and the parametric equation of circle $C$ is
$$
\begin{cases}
x = 10 \cos \theta \\
y = 10 \sin \theta
\end{cases}
(\theta \text{ is the parameter}),
$$
then the length of the chord on circle $C$ cut by line $l$ is ______.

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