
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
Evaluate the product 
\[\left(\frac{1\cdot4}{2\cdot2}\right)\left(\frac{2\cdot5}{3\cdot3}\right)\left(\frac{3\cdot6}{4\cdot4}\right)\cdots\left(\frac{97\cdot100}{98\cdot98}\right)\left(\frac{98\cdot101}{99\cdot99}\right).\]
A) $\frac{1}{2}$
B) $\frac{101}{198}$
C) $\frac{100}{198}$
D) $\frac{101}{99}$
E) $\frac{100}{99}$

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