
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
Karol uses Gluze and Blurpos to make Zippies. His recipe uses 4 cups of Gluze and 3 cups of Blurpos to make 60 Zippies. He can also make larger batches of Zippies using these same ratios.
(a) On Monday, Karol uses 28 cups of Gluze when he makes Zippies. Determine the number of cups of Blurpos that he uses.
(b) On Tuesday, Karol uses 48 cups of one of the ingredients and $N$ cups of the other ingredient when he makes Zippies. Determine the two possible values of $N$.
(c) On Wednesday, Karol has 64 cups of Gluze and 42 cups of Blurpos available. Determine the largest number of Zippies that he can make.
(d) On Thursday, Karol makes Zippies to sell. His only costs come from purchasing Gluze and Blurpos. He sells each Zippie for $\$ 0.50$ and makes a profit of $\$ 0.30$ from each Zippie sold. Karol pays $\$ 1.80$ for each cup of Gluze. Determine how much Karol pays per cup of Blurpos.

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