
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 that the modified iterative average of the numbers 1, 2, 3, 4, and 6 is computed as follows: Arrange the five numbers in any order. Add 1 to the first number, square the second number, and find the factorial of the third number before averaging. Find the average of the modified first two numbers, then the average of that with the modified third number, then the average of that with the fourth number, and finally the average of that with the fifth number.

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