
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
Eight distinct points, $P_1$, $P_2$, $P_3$, $P_4$, $P_5$, $P_6$, $P_7$, and $P_8$, are evenly spaced around a circle. If four points are chosen at random from these eight points to form two chords, what is the probability that the chord formed by the first two points chosen intersects the chord formed by the last two points chosen?

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