
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 gas station has two output pipes A and B, and one input pipe C. When the tank is empty, opening A (to fuel cars) and C (to fill the tank) simultaneously will fill the tank in 2 hours; if B and C are opened simultaneously instead, it will take 4 hours to fill the tank. When the tank is full, opening A and B simultaneously for 3 hours, and then opening C for 5 hours (with A and B still open), the tank is full again. How many hours will it take to fill the tank when it is empty if only C is opened?

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