
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
Consider a right triangle $ABC$ with $AB = 10$, $BC = 6$, and $C$ as the right angle. A point $P$ is randomly placed within the triangle. What is the probability that both the area of triangle $PBC$ is less than one-third of the area of triangle $ABC$, and the distance of $P$ from side $AB$ is less than $3$ units?

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