
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
In triangle $ABC$, which is a right triangle with legs $AB$ and $AC$, points $P$ and $Q$ are on legs $AB$ and $AC$, respectively, such that $AP:PB = AQ:QC = 2:3$. If $BQ = 18$ units, and $CP = 24$ units, find the length of $AB$.

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