
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 12 horses, named Horse 1, Horse 2, ..., Horse 12. Each Horse $k$ runs one lap around a circular racetrack in exactly $k$ minutes. At time 0, all horses start running from the same point on the track. Let $T>0$ be the least time such that at least 6 of the horses are again at the starting point together. The least time $S>0$ when all 12 horses are at the starting point together is $27720$ minutes. What is the sum of the digits of $T$?
A) 2
B) 3
C) 4
D) 5
E) 6

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