
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
At the elementary school U Tří dubů, where Zikmund attends, they hold an annual knowledge competition in which each participant can earn up to 15 points. This year, the average score of the contestants, rounded to the nearest tenth, was 10.4. After the competition, Zikmund realized that he had misunderstood one question and answered something else. He could have scored 4 points more, and the average score rounded to the nearest tenth would have increased to 10.6.

Determine the minimum and maximum number of children who competed this year at U Tří dubů.

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