
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
Petya plans to spend all 90 days of his vacation in the village. Every second day (i.e., every other day), he goes swimming in the lake. Every third day, he goes to the store for groceries. Every fifth day, he solves math problems. (On the first day, Petya did all three activities and was very tired.) How many "pleasant" days will Petya have, when he has to go swimming but does not need to go to the store or solve problems? How many "boring" days will there be when there are no activities at all?

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