
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
The set \( S \) consists of 9 distinct positive integers. The average of the two smallest integers in \( S \) is 5 and the average of the two largest integers in \( S \) is 22. Calculate the greatest possible average of all of the integers of \( S \).

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