
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
Professor Lorena taught her students the following notable product: for any real numbers $a$ and $b$,

$$
a^{2}-b^{2}=(a+b)(a-b)
$$

For example, $4^{2}-3^{2}=16-9=7$. On the other hand, $(4+3)(4-3)=7 \times 1=7$. Using this teaching of Professor Lorena,

a) Calculate

$$
100^{2}-99^{2}+98^{2}-97^{2}+96^{2}-95^{2}+\cdots+2^{2}-1^{2}
$$

b) Find two integers greater than 1 whose product is 999,991.

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