
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
The parametric equations of curve $C_1$ are $$\begin{cases} x=-1+2\cos\theta \\ y=2\sin\theta \end{cases}$$ ($\theta$ is the parameter), and the polar equation of curve $C_2$ is $\rho=2$, with the pole as the origin and the positive semi-axis of the x-axis as the polar axis. Then, the equation of the line containing the common chord of curves $C_1$ and $C_2$ in the Cartesian coordinate system is __________.

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