
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
Let \( P \) be a point outside of circle \( O \). A segment is drawn from \( P \) such that it is tangent to circle \( O \) at point \( T \). Meanwhile, a secant from \( P \) intersects \( O \) at \( A \) and \( B \), where \( PA < PB \). If \( PA = 4 \) and \( PT = 2(AB - PA) \), what is \( PB \)?

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