
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
In a farm's feeding program, each animal must receive at least 45 g of nutrient $A$, at least 60 g of nutrient $B$, and at least 5 g of nutrient $C$ per day. Water consumption is neutral. The farm has two types of feed. The first feed contains $10 \mathrm{g}$ of $A$, $10 \mathrm{g}$ of $B$, and $80 \mathrm{g}$ of water per kilogram, and the second feed contains $10 \mathrm{g}$ of $A$, $20 \mathrm{g}$ of $B$, $5 \mathrm{g}$ of $C$, and $65 \mathrm{g}$ of water per kilogram.

a) What feeding program will minimize the cost if the first feed costs $30 \mathrm{Ft} / \mathrm{q}$ and the second costs $120 \mathrm{Ft} / \mathrm{q}$?

b) What feeding program will minimize the feeding loss if the first feed has a 10% loss and the second has a 20% loss?

c) Is there a feeding program that meets both requirements simultaneously, and what does one animal receive in that case?

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