
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
We have three containers of equal volume and a pipette. The first container is half-filled with a water-soluble liquid, while the second and third containers are empty. From the first container, we transfer a full pipette of liquid into the second container. Then, we add water to the second container to make it half-full. After mixing, we transfer a full pipette of this solution to the third container, fill it halfway with water, and mix it. We then use this new mixture to fill the first container halfway, and the remaining mixture is poured into the second container. Now, the first and second containers contain mixtures with equal dilution. What fraction of the containers' volume is the volume of the pipette?

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