
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 $Q$ is selected at random from the interior of the pentagon with vertices $F=(0,1)$, $G=(3,0)$, $H=(2\pi + 2, 0)$, $I=(2\pi + 2, 3)$, and $J=(0,3)$. What is the probability that $\angle FQG$ is obtuse?

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