
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's start by calculating the value of $(100+2) \times (100-2)$:  
$(100+2) \times (100-2) = 100 \times 100 - 2 \times 100 + 2 \times 100 - 4$  
$= 100^2 - 2^2$.  
This is a calculation with specific numbers. If we replace $100$ with the letter $a$ and $2$ with the letter $b$, the above calculation process becomes  
$(a+b)(a-b) = a^2 - ab + ab - b^2 = a^2 - b^2$.  
Thus, we have derived an important formula  
$(a+b)(a-b) = a^2 - b^2$, (1)  
This formula is called the difference of squares formula.  
(1) Use this formula to calculate $3001 \times 2999$  
(2) Calculate $(2+1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)(2^{32}+1)$.

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