
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 positive real solutions \((a, b, c, d)\) of the equation

\[
\frac{a^{2}-bd}{b+2c+d}+\frac{b^{2}-ca}{c+2d+a}+\frac{c^{2}-db}{d+2a+b}+\frac{d^{2}-ac}{a+2b+c}=0
\]

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