
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 \(xOy\), with \(O\) as the pole and the positive half-axis of the \(x\)-axis as the polar axis, the polar equation of curve \(C_1\) is \(ρ=1\), and the polar equation of curve \(C_2\) is \(ρ=4\cos θ\).

(1) Find the rectangular coordinates of the intersection points of curves \(C_1\) and \(C_2\).

(2) If a line \(l\) is tangent to both \(C_1\) and \(C_2\), find the equation of line \(l\).

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