
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, the coach of country $F$ wants to evaluate players $A_{1}, A_{2}, \cdots, A_{7}$ by having them participate in 3 training matches (each lasting 90 minutes). During these matches, only one player is on the field at any given time. Players $A_{1}, A_{2}, $A_{3}, $ and $A_{4}$ each spend a total amount of time on the field (in minutes) that is divisible by 7. Players $A_{5}, A_{6}, $ and $A_{7}$ each spend a total amount of time on the field (in minutes) that is divisible by 13. If there are unlimited substitutions during each match, how many different possible 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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