
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 to Horse 12, with each horse k taking k minutes to complete a lap around a circular racetrack. However, the horses start at staggered times—Horse k starts k seconds after the previous horse. Determine the least time $U > 0$, in minutes, such that at least 7 of these horses are simultaneously back at the starting point.
A) 210
B) 280
C) 360
D) 420
E) 504

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