
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, Alice and Bob, go to a park independently at random times between 8 a.m. and 9 a.m. Each stays for exactly $n$ minutes. The probability that one arrives while the other is still at the park is $30\%$. Express $n$ in the form $p - q\sqrt{r}$, where $p$, $q$, and $r$ are positive integers, and $r$ is not divisible by the square of any prime. Find $p + q + r$.

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