
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
Place the numbers \( 663, 664, 665, 666, 667, 668, 669, 670, \) and \( 671 \), without repetition, in a \( 3 \times 3 \) grid such that the sum of each row, each column, and each diagonal is 2001. If this is not possible, justify your answer.

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