
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
1. (a) Determine the average of the six integers \(22, 23, 23, 25, 26, 31\).

(b) The average of the three numbers \(y+7, 2y-9, 8y+6\) is 27. What is the value of \(y\)?

(c) Four positive integers, not necessarily different and each less than 100, have an average of 94. Determine, with explanation, the minimum possible value for one of these integers.

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