
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
Two friends decide to meet for a chess game every day. They arrive at the park independently, at random times between 3 p.m. and 4 p.m., and stay for exactly \( n \) minutes. The probability that either one arrives while the other is at the park is \( 25\% \), and \( n = d - e\sqrt{f} \), where \( d, e, \) and \( f \) are positive integers, and \( f \) is not divisible by the square of any prime. Find \( d + e + f \).

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