
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 $\rho=10\cos\theta$. Find the distance $|AB|$ between the two intersection points $A$ and $B$ of the curves $C_{1}$ and $C_{2}$.

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