
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
Petr, Martin, and Jirka were hitting a special target with three fields of different values. Each boy threw a total of ten times and always hit the target. The point scores from the first eight throws were the same for all three boys. In the last two throws, Jirka hit the field with the smallest possible value twice, Martin hit the field with the middle value twice, and Petr hit the field with the highest value twice. The arithmetic average of all of Martin’s throws was 1 more than Jirka's average, and Petr’s average was 1 more than Martin’s average.

Determine all possible values of the fields on the target, knowing that one of them was 12. 

(E. Novotná)

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