
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
Circles $O\_1$ and $O\_2$ have polar equations $ρ = 4\cos(θ)$ and $ρ = -\sin(θ)$ respectively.

(1) Establish a Cartesian coordinate system with the pole as the origin, the polar axis as the positive $x$-axis, and using the same unit length for both coordinate systems. Convert the polar equations of circles $O\_1$ and $O\_2$ into Cartesian equations.

(2) Find the Cartesian equation of the line passing through the intersection points of circles $O\_1$ and $O\_2$.

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