
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 swimming pool can be filled by any of three hoses A, B, or C. Hoses A and B together take 3 hours to fill the pool. Hoses A and C together take 5 hours to fill the pool. Hoses B and C together take 4 hours to fill the pool. How many hours does it take hoses A, B, and C working together to fill the pool? Express your answer as a decimal to the nearest hundredth.

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