
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 distinct real numbers such that
\[\frac{a}{b-c} + \frac{b}{c-a} + \frac{c}{a-b} = -1.\]
Find all possible values of
\[\frac{a^3}{(b-c)^2} + \frac{b^3}{(c-a)^2} + \frac{c^3}{(a-b)^2}.\]

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