
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
John, Bill, and George sold apples side by side one day. In the morning, they sold 2 apples for 5 cents – or 1 apple for \( \frac{5}{2} \) cents – and in the afternoon, they sold 3 apples for 5 cents – or 1 apple for \( \frac{5}{3} \) cents. John sold the same amount in the afternoon as he did in the morning. Bill had the same revenue in the morning and afternoon. George sold apples in the morning and afternoon in the same ratio as \( \frac{5}{3} \) to \( \frac{5}{2} \). What was the average price per apple for each boy? Which formulas give the average price per apple if the morning price is denoted by \( A \) and the afternoon price by \( B \)?

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