
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 games, coach of country $F$ wants to observe the seven players $\mathrm{A}_{1}, \mathrm{A}_{2}, \cdots, \mathrm{A}_{7}$ in three training matches (each match is 90 minutes). Assuming that at any given moment, exactly one of these players is on the field, and players $\mathrm{A}_{1}, \mathrm{A}_{2}, \mathrm{A}_{3}, \mathrm{A}_{4}$ each have total playing time (in minutes) divisible by 7, and players $\mathrm{A}_{5}, \mathrm{A}_{6}, \mathrm{A}_{7}$ each have total playing time (in minutes) divisible by 13. If the number of substitutions is unlimited, how many different total playing time combinations are possible for each player?

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