
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

$$
A = \left( \frac{a+b}{c} \right)^4 + \left( \frac{b+c}{d} \right)^4 + \left( \frac{c+d}{a} \right)^4 + \left( \frac{d+a}{b} \right)^4
$$

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