
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
Four girls played a series of matches. When asked how many matches they won, they gave a very evasive answer:

"If we summed the number of wins for each pair of girls, we would get the numbers $8,10,12,12,14,$ and $16$."

Determine how many wins each girl achieved.

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