
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 Baumé hydrometer shows $5^{\circ}$ when immersed in pure milk. When immersed in milk mixed with water, it shows $2.2^{\circ}$. What is the ratio of milk to water in the mixture if the density of the saline solution used to determine the 15th degree is $1.116$?

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