
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 $p,$ $q,$ $r,$ $s,$ $t,$ $u,$ $v,$ and $w$ be real numbers such that $pqrs = 8$ and $tuvw = 16.$ Find the minimum value of
\[(pt)^2 + (qu)^2 + (rv)^2 + (sw)^2.\]

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