
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
Before the World Cup soccer match, Coach F wants to assess players $A_{1}$, $A_{2}, \cdots, A_{7}$ in three training games (each lasting 90 minutes). Suppose that at any moment in the game, exactly one of these players is on the field, and the total time each of $A_{1}, A_{2}, A_{3}, A_{4}$ spends on the field (in minutes) is divisible by 7, and the total time each of $A_{5}, A_{6}, A_{7}$ spends on the field (in minutes) is divisible by 13. If the number of substitutions is unlimited, how many different scenarios are there based on the total time each player spends on the field?

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