
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 tank can be filled by three pumps: Pump X, Y, and Z. When Pump X and Y work together, they take 3 hours to fill the tank. When Pump X and Z work together, they take 6 hours to fill the tank. When Pump Y and Z work together, they take 4.5 hours to fill the tank. Determine how many hours it will take for all three pumps, X, Y, and Z, to fill the tank together. Express your answer as a fraction.

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