
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
It is known that a straight line l passes through point P(1, 0) with an inclination angle of $\alpha = \frac{\pi}{6}$. The line intersects a circle with equation $x^2 + y^2 = 4$ at points A and B. Find 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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