
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
There are ten horses numbered from 1 to 10. The k-th horse (k = 1, 2, ⋯, 10) takes exactly k minutes to run one lap on a circular track. Initially, all horses start at the starting point of the track at the same time, facing the same direction, and run at their own constant speeds along the circular track. It is known that it takes at least S = 2520 minutes for all ten horses to return to the starting point simultaneously. Let t be the minimum time such that at least five horses are at the starting point simultaneously. Calculate the sum of the digits of t.

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