
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) There are three identical large containers. One contains 3 liters of syrup, another contains 20 liters of water, and the third is empty. You can pour all the liquid from one container into another or into a sink. You can also choose two containers and pour from the third into one of them until the liquid levels in the chosen containers are equal. How can you obtain 10 liters of diluted 30% syrup?

b) The same problem as in part a), but instead of 20 liters of water, there are N liters of water. For which integer values of N can you obtain 10 liters of diluted 30% syrup?

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