
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
Triangle $ABC$ is a right triangle with legs $AB$ and $AC$. Points $X$ and $Y$ lie on legs $AB$ and $AC$, respectively, so that $AX:XB = 1:3$ and $AY:YC = 2:1$. If $BY = 24$ units and $CX = 18$ units, what is the length of hypotenuse $BC$? Express your answer in simplest radical form.

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