
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 students study in a library and each spends exactly $n$ minutes there. They arrive at random times between 3 p.m. and 4 p.m. The probability that one arrives while the other is still in the library is $30\%$. Let $n = d - e\sqrt{f}$, where $d, e, f$ 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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