
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 initially holds 10 kilograms of water. In the first step, $\frac{1}{3}$ of the liquid is removed, and then 1 kilogram of pure alcohol is added. In the second step, $\frac{1}{3}$ of the liquid is removed again, and then $\frac{1}{2}$ kilogram of pure alcohol is added. In subsequent steps, $\frac{1}{3}$ of the liquid is removed, and the added amount of pure alcohol is half of the amount added in the previous step. What is the concentration of the alcohol solution in the container after the $n^{th}$ operation?

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