
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
Find all sets of four positive real numbers \((a, b, c, d)\) satisfying
\[
\begin{array}{l}
a + b + c + d = 1, \\
\text{and} \\
\max \left\{\frac{a^{2}}{b}, \frac{b^{2}}{a}\right\} \max \left\{\frac{c^{2}}{d}, \frac{d^{2}}{c}\right\} = (\min \{a+b, c+d\})^{4}.
\end{array}
\]

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