
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 \( P \) on a triangular piece of paper \( ABC \), consider the creases that are formed when \( A, B, \) and \( C \) are folded onto \( P \). Let us determine \( P \) as a fold point of \( \triangle ABC \) if the creases intersect exactly at the vertices of the triangle. Suppose \( AB = 48, AC = 96 \), and \( \angle B = 90^\circ \). Compute the area of the set of all such fold points of \( \triangle ABC \).

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