
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
A mathematical conjecture states that every square of an odd integer greater than 1 can be written as the sum of two consecutive integers. What would a counterexample to this conjecture consist of?
- The problem statement represents a similar mathematical idea, which will help in understanding the concept of counterexamples through a different scenario.
**A)** an odd integer \( n > 1 \) where \( n^2 \) can be written as the sum of three integers.
**B)** an odd integer \( n > 1 \) where \( n^2 \) can be written as the sum of two consecutive integers.
**C)** an even integer \( n > 1 \) where \( n^2 \) can be written as the sum of two consecutive integers.
**D)** an odd integer \( n > 1 \) where \( n^2 \) cannot be written as the sum of two consecutive integers.
**E)** an even integer \( n > 1 \) where \( n^2 \) cannot be written as the sum of two consecutive integers.

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