
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
Taking the origin of the Cartesian coordinate system as the pole and the positive half-axis of the x-axis as the polar axis, and using the same length scale in both coordinate systems. The polar equation of curve $C_1$ is $\rho=2\cos\theta$. Curve $C_1$ is translated one unit to the left and then its x-coordinate is stretched to twice its original length to obtain curve $C_2$.
(1) Find the Cartesian equation of curve $C_2$;
(2) A line passing through point P(1, 2) intersects curve $C_2$ at points A and B. Find the minimum value of $|PA||PB|$.

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