
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 positive numbers \(a, b, c\) such that
\[
a^{2}(a-1) + b^{2}(b-1) + c^{2}(c-1) = a(a-1) + b(b-1) + c(c-1),
\]
find the value of \(1956 a^{2} + 1986 b^{2} + 2016 c^{2}\).

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