
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 $8$ horses, each with different speeds. Horse $k$ takes $k^2$ minutes to run one lap on the track, where $k$ is the horse number from $1$ to $8$. At time $0$, all horses are at the starting point. They start running together at constant speeds. Let $S > 0$ be the time in minutes when at least $4$ of the horses are again at the starting point together. Find $S$.
A) 100
B) 144
C) 225
D) 256
E) 400

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