
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 competition, coach $F$ of country $F$ plans to evaluate the seven players $A_{1}, A_{2}, \cdots, A_{7}$ by letting them play in three training matches (each 90 minutes long). Assuming that at any given moment during the match, exactly one of these players is on the field, and the total playing time (in minutes) for each of $A_{1}, A_{2}, A_{3}, A_{4}$ is divisible by 7, and the total playing time (in minutes) for each of $A_{3}, A_{5}, A_{6}, A_{7}$ is divisible by 13, how many different configurations are there in terms of each player's total playing time?

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