
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
Given a point $Q$ on a rectangular piece of paper $DEF$, where $D, E, F$ are folded onto $Q$. Let $Q$ be a fold point of $\triangle DEF$ if the creases, which number three unless $Q$ is one of the vertices, do not intersect within the triangle. Suppose $DE=24, DF=48,$ and $\angle E=90^\circ$. Determine the area of the set of all possible fold points $Q$ of $\triangle DEF$.

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