
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
Let R<sub>A</sub>, R<sub>B</sub>, and R<sub>C</sub> denote the rates of flow at which valves A, B, and C fill the tank, respectively. When all three valves are opened, it takes 1 hour to fill the tank, so the combined rate is R = R<sub>A</sub> + R<sub>B</sub> + R<sub>C</sub>. When only valves A and C are opened, it takes 1.5 hours to fill the tank, so the combined rate is R<sub>A</sub> + R<sub>C</sub> = 2R/3. When only valves B and C are opened, it takes 2 hours to fill the tank, so the combined rate is R<sub>B</sub> + R<sub>C</sub> = R/2. If only valves A and B are opened, find the time it will take to fill the tank.

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