
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 line \( l \) tangent to the unit circle \( S \) at point \( P \), point \( A \) lies on the same side of \( l \) as circle \( S \), and the distance from \( A \) to \( l \) is \( h \) where \( h > 2 \). From point \( A \), two tangents to \( S \) are drawn, intersecting \( l \) at points \( B \) and \( C \). Find the product of the lengths of line segments \( PB \) and \( PC \).

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