
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 using any of three hoses labeled A, B, or C. Working together, hoses A and B can fill the pool in 5 hours. Hoses A and C can fill it in 6 hours, and hoses B and C can fill it in 7.5 hours. Determine how many hours it will take for hoses A, B, and C working together to fill the pool. Express your answer as a fraction.

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