
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:
\[
\left(\frac{1\cdot 4}{2\cdot 2}\right)\left(\frac{2\cdot 5}{3\cdot 3}\right)\left(\frac{3\cdot 6}{4\cdot 4}\right)\cdots\left(\frac{98\cdot 101}{99\cdot 99}\right)\left(\frac{99\cdot 102}{100\cdot 100}\right)
\]
A) $\frac{102}{100}$
B) $\frac{51}{50}$
C) $\frac{100}{99}$
D) $\frac{50}{99}$
E) $\frac{99}{100}$

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