
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 79 trainees of the Animath workshop each choose an activity for the free afternoon among 5 offered activities. It is known that:

- The swimming pool was at least as popular as soccer.
- The students went shopping in groups of 5.
- No more than 4 students played cards.
- At most one student stayed in their room.

We write down the number of students who participated in each activity. How many different lists could we have written?

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