
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 that the vertices of a pentagon are  $ A \equal{} (0,2)$ ,  $B \equal{} (4,0)$ ,  $C \equal{} (2 \pi \plus{} 1, 0)$ ,  $D \equal{} (2 \pi \plus{} 1,4)$ , and  $E \equal{} (0,4)$ , determine the probability that the angle formed by the line segment joining a randomly selected point $P$ from the interior of the pentagon to point $B$ is obtuse.

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