
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 $ABC$, where $AB=45$, $AC=90$, and $\angle B=90^\circ$, find the area of the region where point $P$ can be a fold point of $\triangle ABC$. A point $P$ is a fold point if the creases formed when $A, B,$ and $C$ are folded onto $P$ do not intersect inside the triangle.

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