
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 $xOy$, the parametric equation of curve $C_1$ is $$\begin{cases} x=6+ \frac { \sqrt {3}}{2}t \\ y= \frac {1}{2}t\end{cases}$$ (where $t$ is the parameter); in the polar coordinate system with $O$ as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of curve $C_2$ is $\rho=10\cos\theta$. Curves $C_1$ and $C_2$ intersect at points $A$ and $B$. Find $|AB|$.

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