
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
The values of \( f, g, h, j \) are 2, 4, 6, and 8, but not necessarily in that order. Assuming the sum \( f+g+h+j \) remains constant, what is the maximum possible value of \( f^2+g^2+h^2+j^2 \), and what is the corresponding value of \( fg+gh+hj+fj \)?

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