
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
Six numbers, 1 through 6, are arranged in some order. Calculate the iterative average in the following way: start by finding the mean of the first two numbers, then find the mean of that result with the third number, and continue this way until the sixth number is included. What is the difference between the largest and smallest possible values that can be obtained using this procedure?
A) $\frac{23}{8}$
B) $\frac{49}{16}$
C) $\frac{65}{16}$
D) $\frac{31}{16}$
E) $\frac{17}{8}$

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