
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
At the bus stop near the Absent-Minded Scientist's house, buses of two routes stop: No. 152 and No. 251. Both go to the metro station. The interval between buses No. 152 is exactly 5 minutes, and the interval between buses on route 251 is exactly 7 minutes. The intervals are strictly maintained, but these two routes are not coordinated with each other, and their schedules do not depend on each other. At a completely random moment in time, the Absent-Minded Scientist arrives at the bus stop and boards the first bus that comes to take him to the metro. What is the probability that the Scientist will board bus No. 251?

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