
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
From a container filled with 20 liters of pure alcohol, 1 liter is poured out and then the container is refilled with water. This process of pouring out 1 liter of the mixed solution and refilling with water is repeated. If, after the $k$-th time $(k \geq 1)$, a total of $x$ liters of pure alcohol has been poured out, find the expression for the function $f(x)$ that represents the total amount of pure alcohol poured out after the $(k+1)$-th time.

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