
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
Suppose three hoses, X, Y, and Z, are used to fill a pool. Hoses X and Y together take 3 hours, while hose Y working alone takes 9 hours. Hoses X and Z together take 4 hours to fill the same pool. All three hoses working together can fill the pool in 2.5 hours. How long does it take for hose Z working alone to fill the pool?

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