
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 1, 2, 3, 4, 5, and 6, arrange these six numbers in some order. Find the mean of the first two numbers, then find the mean of that result with the third number, continue this process until the fifth number. For the final step, add 2 to the result before averaging it with the sixth number. Calculate the difference between the largest and smallest possible values that can be obtained using this procedure.

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