
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 scientists visit an observatory to watch the stars. They arrive independently at random times between 10 p.m. and midnight, and each stays for exactly $n$ minutes. The probability that either one arrives while the other is there is $30 \%$. Given $n = x - y\sqrt{z},$ where $x, y,$ and $z$ are positive integers, with $z$ not divisible by the square of any prime, find $x + y + z.$

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