
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, $\ldots$, Horse 12. Each Horse $k$ runs one lap around a circular race track in exactly $k^2$ minutes. At time 0, all the horses are together at the starting point on the track. The horses start running in the same direction at their constant speeds. Let $T > 0$ be the least time, in minutes, such that exactly $6$ of these horses are again at the starting point together. Calculate 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