
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
Given positive numbers \(a, b, c, d\), find the minimum value of the expression

$$
A=\left(\frac{a^{2}+b^{2}}{cd}\right)^{4}+\left(\frac{b^{2}+c^{2}}{ad}\right)^{4}+\left(\frac{c^{2}+d^{2}}{ab}\right)^{4}+\left(\frac{d^{2}+a^{2}}{bc}\right)^{4}
$$

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