
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
Ivan the Prince has two containers, each with a capacity of 1 liter. One is completely filled with ordinary water, and the other contains $a$ liters of living water, where $0 < a < 1$. He can transfer any volume of liquid from one container to another up to any level without overflowing and wants to obtain a 40% solution of living water in one of the containers after a finite number of such transfers. For which values of $a$ can Ivan the Prince achieve this? Assume that the liquid level in each container can be measured exactly at any time.

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