
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 $$\begin{cases} \left.\begin{matrix}x=2-t \\ y=2t\end{matrix}\right.\end{cases}$$ (where $t$ is the parameter). In the polar coordinate system (using the same unit length as the Cartesian coordinate system xOy, and taking the origin O as the pole and the positive x-axis as the polar axis), the polar equation of curve $C_2$ is $\rho=4\cos\theta$. The distance between the two intersection points of $C_1$ and $C_2$ is \_\_\_\_\_\_.

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