
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 rectangular coordinate system $xOy$, the parametric equations of the curve $C_1$ are given by $\begin{cases} x=6+\frac{\sqrt{3}}{2}t \\ y=\frac{1}{2}t \end{cases}$ ($t$ is the parameter). In the polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis, the polar equation of the curve $C_2$ is given by $\rho=10\cos \theta$. The curves $C_1$ and $C_2$ intersect at points $A$ and $B$.
(I) Write the Cartesian equations for $C_1$ and $C_2$.
(II) Calculate the distance $|AB|$.

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