
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 $O$ with radius $r$. A tangent from $P$ to circle $O$ touches it at point $T$. A secant from $P$ intersects $O$ at points $A$ and $B$ (with $PA < PB$). If $PA = 4$ and $PT = AB - 2$, find the length $PB$.

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