
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
Let the cost of each bookmark be x cents. Let the number of fifth graders bought bookmarks be y. A group of fifth graders bought a total of 2.25 dollars or 225 cents. Since the cost of each bookmark is x cents, then the equation is y*x=225. Let the number of fourth graders bought bookmarks be z. A group of fourth graders bought a total of 2.60 dollars or 260 cents. Since the cost of each bookmark is x cents, then the equation is z*x=260. The difference between the number of fourth graders and the fifth graders bought bookmarks is z-y, and since we have two equations, we can find the number of fourth graders and fifth graders bought bookmarks and express z-y in terms of x.

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