
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 $B$, such that $PA < PB$. If $PA = 5$ and $PT = AB - 2 \cdot PA$, then what is $PB$?

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