
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 $a$ and $b$ be positive integers such that $a > b$, and some computation requires an estimate of $a^2 - b^2$. Mahesh plans to make an estimate by rounding $a$ down by a small integer $d$ and rounding $b$ up by the same integer $d$. What can be concluded about Mahesh's estimate compared to the true value of $a^2 - b^2$?
A) Mahesh's estimate is greater than the true value of $a^2 - b^2$
B) Mahesh's estimate is less than the true value of $a^2 - b^2$
C) Mahesh's estimate equals the true value of $a^2 - b^2$
D) Mahesh's estimate equals the negative of the true value of $a^2 - b^2$
E) Mahesh's estimate is zero

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