
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
Rita, Lyuba, and Varya were solving problems. To make the process faster, they bought candies and agreed that for each solved problem, the girl who solved it first would receive four candies, the one who solved it second would get two candies, and the one who solved it last would get one candy. The girls claimed that each of them solved all the problems and received 20 candies, and moreover, no problems were solved simultaneously. Why do you think they are mistaken?

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