
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 container holds one liter of wine, and another holds one liter of water. From the first container, we pour one deciliter into the second container and mix thoroughly. Then, we pour one deciliter of the mixture back into the first container. Calculate the limit of the amount of wine in the first container if this process is repeated infinitely many times, assuming perfect mixing with each pour and no loss of liquid.

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