
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 iterative process of calculating the mean of the first two numbers, then the mean of that result with the third number, and continuing this process until all numbers are included, using the numbers 1, 2, 3, 4, 5, and 6, find the difference between the largest and smallest possible values that can be obtained.

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