
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
The numbers \(a, b,\) and \(c\) (not necessarily integers) are such that:

\[
a + b + c = 0 \quad \text{and} \quad \frac{a}{b} + \frac{b}{c} + \frac{c}{a} = 100
\]

What is the value of \(\frac{b}{a} + \frac{c}{b} + \frac{a}{c}\)?

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