
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
Arrange the numbers 2, 3, 5, 7, and 11 in any order. An iterative average is computed by finding the mean of the first two numbers, then computing the mean of that result with the third number, and continuing this method until the mean with the fifth number is computed. Calculate the difference between the largest and smallest possible values that can be obtained through this method.

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