
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
Given the numbers 4, 5, 6, 7, and 8, compute the largest and smallest possible values that can be obtained from an iterative averaging process, starting by averaging the first three numbers and continuing by adding the next numbers one by one, and calculate the difference between these maximal and minimal values.

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