
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
Consider two sequences: one in increasing order, 1, 2, 3, 4, 5, and one in alternating order of magnitude, 5, 4, 3, 2, 1. Compute the iterative average for both sequences and determine the difference between the largest and smallest possible values that can be obtained.

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