
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
Consider a race with $8$ horses named Horse 1 through Horse 8, where Horse $k$ completes a lap in $k$ hours. All the horses start simultaneously from a starting point. Determine the least time $T > 0$, in hours, such that exactly half of these horses will be together again at the starting point.

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