
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 62 trainees at the Animath camp each take an ice cream among 5 proposed flavors. It is known that:

- The bubblegum flavored ice cream was at least as popular as the tabasco flavored ice cream;
- The number of students who chose cactus flavored ice cream is a multiple of 6;
- At most 5 students tasted lemon basil flavored ice cream;
- At most one student chose foie gras flavored ice cream.

When Igor places the order with the ice cream vendor, he communicates, in alphabetical order of the flavors, the number of students who chose each flavor. How many different lists of numbers could he have announced?

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