
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, and 5, find the difference between the largest and smallest possible values that can be obtained using the iterative process to compute the modified average as described.

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