
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
Given the polar equation of curve C is $\rho^2 - 4\rho\cos\theta - 2\rho\sin\theta = 0$. Taking the pole as the origin of the Cartesian coordinate system, and the polar axis as the positive x-axis, establish the Cartesian coordinate system xOy. In the Cartesian coordinate system, a line passes through point P(1, 2) with an inclination angle of $\frac{\pi}{6}$.
(1) Write the Cartesian equation of curve C and the parametric equation of the line;
(2) Suppose the line intersects curve C at points A and B, find the value of $|PA| \cdot |PB|$.

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