
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
A straight line l passes through point P(1, 1) with an inclination angle of α, and $\tan \alpha = \frac{3}{4}$.
(1) Write a parametric equation for line l.
(2) Assuming l intersects the circle $x^2+y^2=4$ at two 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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