
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 83 trainees from the Animath workshop each choose an activity for the free afternoon from 5 activities offered. We know that:

$\triangleright$ Shopping was at least as popular as Laser Tag;

$\Delta$ Movie tickets are sold in batches of 6;

$\Delta$ At most 5 students go to the beach;

$\triangleright$ At most one student visited a Romanesque church.

When writing the list of activities in alphabetical order, the number of students corresponding to each activity is written. How many different lists of numbers can be written?

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