
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
A similar iterative average process is used, but this time with six numbers: 0, 1, 2, 3, 4, and 5. Arrange the six numbers in any sequence. Calculate the average of the first two numbers, then average that result with the third number, continue this process until the sixth number. What is the difference between the largest and smallest possible values obtained from this procedure?
A) 1.5625
B) 2.0000
C) 2.125
D) 2.5625
E) 3.0000

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