
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
Suppose $a,$ $b,$ and $c$ are real numbers such that
\[\frac{ac}{a+b} + \frac{ba}{b+c} + \frac{cb}{c+a} = -12\] and
\[\frac{bc}{a+b} + \frac{ca}{b+c} + \frac{ab}{c+a} = 15.\] Compute the value of
\[\frac{b}{a+b} + \frac{c}{b+c} + \frac{a}{c+a}.\]

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