
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
The stable has $12$ horses, each named Horse 1 to Horse 12, where each Horse $k$ runs one lap in exactly $k$ minutes. At time 0, all the horses are together at the starting point. The least time $S > 0$, in minutes, at which all $12$ horses will again simultaneously be at the starting point is $S = 27720$. Determine the least time $T > 0$, such that at least $9$ horses are at the starting point again. What is the sum of the digits of $T$?
A) 6 
B) 7 
C) 8 
D) 9
E) 10

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