
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 a straight line $l$ passes through the point $P(1, 1)$ with an inclination angle of $α = \frac{\pi}{6}$,
(1) Write the parametric equations of line $l$.
(2) Suppose line $l$ intersects the circle $x^2 + y^2 = 4$ at two points $A$ and $B$. Calculate the product of the distances from point $P$ to points $A$ and $B$.

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