
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 the seven players $A_{1}, A_{2}, \cdots, A_{7}$ by letting them play in three training matches (each lasting 90 minutes). Suppose that at any moment during the matches, exactly one of these players is on the field. Additionally, the total playing time (in minutes) for each of players $A_{1}, A_{2}, A_{3}, A_{4}$ is divisible by 7, and the total playing time for each of players $A_{5}, A_{6}, $ and $A_{7}$ is divisible by 13. If there are no restrictions on the number of substitutions, how many different possible situations are there based on the total playing time of each player?

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