
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 football match, the coach of country $F$ wants to evaluate seven players $A_{1}, A_{2}, \cdots, A_{7}$. He plans to let them all play in three training matches (each lasting 90 minutes). Assume that at any time during a match, only one of these players is on the field, and the total playing time (in minutes) for each of $A_{1}, A_{2}, A_{3}, A_{1}$ can be evenly divided by 7, while the total playing time for each of $A_{3}, A_{4}, A_{5}, A_{6}, A_{7}$ can be evenly divided by 13. If the number of substitutions is unrestricted in each match, then how many different possible situations are there when calculating the total playing time for each player?

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