
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 selected at random from the interior of the hexagon with vertices \( A=(0,0) \), \( B=(6,0) \), \( C=(9,3) \), \( D=(6,6) \), \( E=(0,6) \), and \( F=(-3,3) \). What is the probability that \( \angle APB \) is obtuse? Assume \( \angle APB \) is obtuse whenever \( P \) lies within a circle centered at \( (3,3) \) with radius \( 3 \).

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