
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, swimming in the lake every second day (i.e., every other day), going shopping for groceries every third day, and solving math problems every fifth day. (On the first day, Petya did all three tasks and got very tired.) How many "pleasant" days will Petya have, when he needs to swim but does not need to go shopping or solve math problems? How many "boring" days will he have, when he has no tasks at all?

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