
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
Each of the corner fields of the outer square should be filled with one of the numbers \(2, 4, 6\), and \( 8 \), with different numbers in different fields. In the four fields of the inner square, there should be the products of the numbers from the adjacent fields of the outer square. In the circle, there should be the sum of the numbers from the adjacent fields of the inner square.

Which numbers can be written in the circle? Determine all possibilities.

(M. Dillinger)

Hint: Can different fillings of the corner fields lead to the same sum in the circle?

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