
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
In a regular pentagon, each of the 5 sides and 5 diagonals is colored independently red or blue. What is the probability that there exists at least one triangle with vertices from the pentagon's vertices, such that all of its sides are the same color, and furthermore, exactly 3 diagonals are red?
A) \(0.9756\)
B) \(0.9858\)
C) \(0.9979\)
D) \(0.9996\)

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