
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
Now consider a swimming pool that can be filled by any of four hoses A, B, C, or D. The following times are known:
- Hoses A and B together take 3 hours to fill the pool.
- Hoses A and C together take 6 hours to fill the pool.
- Hoses A and D together take 4 hours to fill the pool.
- Hoses B and C together take 9 hours to fill the pool.
- Hoses B and D together take 6 hours to fill the pool.
- Hoses C and D together take 8 hours to fill the pool.
How many hours does it take for hoses A, B, C, and D working together to fill the pool?

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