
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
Given the equations

$$
\begin{aligned}
a+b+c & = 0 \\
A+B+C & = 0 \\
\frac{a}{A}+\frac{b}{B}+\frac{c}{C} & = 0
\end{aligned}
$$

What is the value of the expression

$$
a A^{2} + b B^{2} + c C^{2}?
$$

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