
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
Given there are 12 horses, each running at speeds that take them to complete one lap in $2k-1$ minutes where $k=1$ is Horse 1, find the least time $T>0$ such that at least 6 of the horses are simultaneously at the starting point, and then calculate the sum of the digits of $T$.

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