
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 three pairwise distinct positive integers. If \( \{ a+b, b+c, c+a \} = \{ n^2, (n+1)^2, (n+2)^2 \} \), then what is the minimum value of \( a^2 + b^2 + c^2 \)?

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