
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
Each valve X, Y, and Z fills a tank with water at a constant rate. When all three valves are open, they take 2 hours to fill the tank. When only valves X and Z are open, it takes 3 hours, and with only valves Y and Z open, it takes 4 hours. Determine the time it would take for just valves X and Y to fill the tank.

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