
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
In preparation for the World Cup, Coach F intends to evaluate the seven players \( A_{1}, A_{2}, \cdots, A_{7} \) in three training matches (each lasting 90 minutes). Suppose at any given time during the match, only one of these players is on the field. Furthermore, the total playing time for players \( A_{1}, A_{2}, A_{3}, A_{4} \) (in minutes) is divisible by 7, and the total playing time for players \( A_{5}, A_{6}, A_{7} \) (in minutes) is divisible by 13. If the number of substitutions is unlimited, how many different scenarios are there based on the total playing time for each player?

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