
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 real numbers such that \(abcd = 16\) and \(efgh = 1.\) Find the minimum value of:
\[(af)^2 + (be)^2 + (ch)^2 + (dg)^2.\]

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