
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 $DEF$ is a right triangle with legs $DE$ and $DF$. Points $P$ and $Q$ lie on legs $DE$ and $DF$, respectively, so that the length ratios $DP:PE = DQ:QF = 1:3$. If $QE = 18$ units and $PF = 30$ units, find the length of the hypotenuse $EF$. Express your answer in simplest radical form.

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