
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
A cyclist arrived from point \( A \) to point \( B \) on time, traveling at a certain speed. If he had increased his speed by 3 km/h, he would have arrived at the destination an hour earlier, and if he had traveled 2 km/h less than he actually did, he would have been an hour late. Determine the distance between points \( A \) and \( B \), the cyclist's speed, and the travel time.

For the care of horses, a stock of hay was made for a certain period of time. If there had been two fewer horses, the stock of hay would have lasted 10 more days; if there had been two more horses, the stock of hay would have lasted 6 days less than the scheduled time. How many horses were there, and for how many days was the stock of hay made?

The first pipe fills the pool in half the time it takes for the second pipe to fill \(\frac{2}{3}\) of the pool. The second pipe alone fills the pool 6 hours longer than the first pipe. How long does each pipe take to fill the pool individually?

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