
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
Two women were selling apples. One sold three apples for a cent, and the other sold two apples for a cent. At one point, they had to leave and each had 30 unsold apples left, which they entrusted to their friend to sell at two cents for five apples. If the women had sold the remaining apples themselves, they would have received 25 cents, but as it happened, they only received 24 cents. Where did the missing cent go? Selling three apples for a cent and two apples for a cent should be the same as selling five apples for two cents. Could you explain this simple puzzle?

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