
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, each taking unique prime minutes to complete a lap: $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37$ minutes respectively. Determine the least time $T > 0$, in minutes, where at least $6$ horses are back at the starting point again together, and calculate the sum of the digits of $T$.

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