
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
Let \( a, b, c, d, e, f, g, \) and \( h \) be distinct elements in the set 
\[
\{-8, -6, -4, -1, 1, 3, 5, 14\}.
\]
What is the minimum possible value of 
\[
(a+b+c+d)^2 + (e+f+g+h)^2
\]
if it is known that \( e+f+g+h = 9 \)?

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