
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
The 15 supervisors go on a training trip together. Each day, 3 supervisors oversee the swimming pool. We observe that each pair of supervisors has overseen the swimming pool together exactly once. How many days will the training trip last?

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