
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
An isosceles right triangle $ABC$, with $AB = AC = 10$ units and right angle at $A$, is given. A point $P$ is randomly placed in the interior of this triangle. What is the probability that the area of triangle $PBC$ is less than $\frac{1}{4}$ of the area of triangle $ABC$? Draw the line segment from $A$ perpendicular to $BC$ to form right angles.

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