
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
To treat a patient, two types of medicine are available. The first medicine contains 3, 1, 1, and 0 units per tablet of vitamins $A, B, C,$ and $D$ respectively, while the second medicine contains 0, 1, 3, and 2 units per tablet of these vitamins. The patient's daily vitamin requirement is 3 units of $A$, 9 units of $B$, 15 units of $C$, and 2 units of $D$. Determine:

I. The minimum number of tablets the patient needs to take daily, specifying how many of each type of medicine.

II. When the treatment is the cheapest, given that each tablet of the first medicine costs 20 fillér and each tablet of the second medicine costs 60 fillér.

III. If a tablet of the first medicine is absorbed twice as fast as a tablet of the second medicine, what choice allows for the fastest absorption?

IV. Is there a choice that is optimal in all three aspects?

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