
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
With all three valves open, the tank is filled at a rate proportional to the sum of their individual rates, so the combined rate of valves X, Y, and Z is 1/2 of the tank per hour. If only valves Y and Z are open, the rate is 1/3 of the tank per hour, so the rate of valve Y alone is 1/3 - 1/4 = 1/12 of the tank per hour. Let the rate of valve X be x, and the rate of valve Z be z. Then, the rate of valve X is 1/2 - 1/4 - 1/12 = 2/3 - 1/12 = 7/12 of the tank per hour. What is the time it takes for only valves X and Y to fill the tank?

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