
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
Point $P$ is randomly chosen from the interior of the rectangle with vertices $A = (0, 4)$, $B = (5, 0)$, $C = (5, 6)$, and $D = (0, 6)$. What is the probability that $\angle APB$ is obtuse? Assume that $\angle APB = 90^{\circ}$ if and only if $P$ lies on the semicircle centered at the midpoint $(2.5, 2)$ of $AB$, with radius $4.5$ units.

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