
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 wine mixture. One vessel is filled with wine to $\frac{1}{3}$ of its capacity, and another vessel of the same capacity is filled to $\frac{1}{4}$. Both vessels are then topped up with water, and all their contents are mixed in a jug. Half of the resulting mixture is then poured back into one of the two vessels.

What is the ratio of wine to water in that vessel after this process?

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