
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 \( a, b, c \) be nonzero real numbers such that \( a^2 + b^2 + c^2 = ab + bc + ca \). Find all possible values of
\[
\frac{a^2 b^2}{(a^2 + bc)(b^2 + ac)} + \frac{a^2 c^2}{(a^2 + bc)(c^2 + ab)} + \frac{b^2 c^2}{(b^2 + ac)(c^2 + ab)}.
\]

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