
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
Several people participated in an intelligence contest game, which consisted of 3 questions: the first question was worth 20 points, and the next two were each worth 25 points. For each question, a participant could either get the full score by answering correctly or get 0 points for a wrong answer. The statistical results at the end were as follows: every participant answered at least one question correctly, only one person answered all three questions correctly, and 15 people answered two questions correctly. Additionally, the sum of the number of people who answered the first question correctly and the number of people who answered the second question correctly was 29, the sum for the second and third questions was 20, and the sum for the first and third questions was 25. Calculate the average score of this contest.

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