
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
Find numbers \(a, b, c\) such that for every positive integer \(n\) the equation

\[
(n+3)^{2}=a \cdot(n+2)^{2}+b \cdot(n+1)^{2}+c \cdot n^{2}
\]

holds true.

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