
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 go to study in the library each day independently, opting for times between 4 p.m. and 6 p.m., and each stays for exactly $n$ minutes. The probability that one student arrives while the other is studying there is $25\%.$ Calculate $n$, given it is expressed as $d - e\sqrt {f},$ where $d, e$, and $f$ are positive integers, and $f$ is not a perfect square.

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