
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, 4, 6, 8, 10, and 12 in any order, then find the difference between the largest and smallest possible values that can be obtained by computing the iterative average.

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