
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
Is it possible to divide the 8 natural numbers \(1, 2, 3, 4, 5, 6, 7, 8\) into two groups of 4 numbers each so that the sum of the numbers in the first group equals the sum of the numbers in the second group, and the sum of the squares of the numbers in the first group equals the sum of the squares of the numbers in the second group?

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