
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 through Horse 12, each with running times of 1 through 12 minutes respectively to complete one lap around a track. All horses start from the starting point at time 0 and run at constant speeds in the same direction around the track. Determine the least time \( T > 0 \) minutes such that at least 6 of these horses are simultaneously at the starting point again. What is the sum of the digits of \( T \)?
A) 3
B) 4
C) 5
D) 6
E) 7

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