
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 a Cartesian coordinate system, the parameterized equation of line $l$ is given by
$$
\begin{cases}
x = 2 + \frac{\sqrt{3}}{2}t \\
y = \frac{1}{2}t
\end{cases}
$$
where $t$ is the parameter. The line $l$ is intersected by the curve $C$ with the polar equation $\rho = 2\cos\theta$, which has the origin as its pole and the positive x-axis as its polar axis. Find the length of the chord of $C$ cut by $l$.

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