
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
If $a$ and $b$ are odd integers, which of the following is guaranteed to be an odd integer?
- **A)** $a + 2b + 1$
- **B)** $5a - 2b + 2$
- **C)** $(ab + 2)^2$
- **D)** $3a^2 + b^2$
**A)** $a + 2b + 1$
**B)** $5a - 2b + 2$
**C)** $(ab + 2)^2$
**D)** $3a^2 + b^2$

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