
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 \( a, b, c, d \) be non-negative real numbers, satisfying
\[
\frac{a}{b+c+d} = \frac{b}{a+c+d} = \frac{c}{a+b+d} = \frac{d}{a+b+c},
\]

then find the value of \( \frac{a+b}{c+d} + \frac{b+c}{a+d} + \frac{c+d}{a+b} + \frac{d+a}{b+c} \).

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