
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 $a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p$ be real numbers such that $abcd = 16$, $efgh = 16$, $ijkl = 16$, and $mnop = 16$. Find the minimum value of 
\[
(aeim)^2 + (bfjn)^2 + (cgko)^2 + (dhlp)^2.
\]

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