
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:
\[
\left(\frac{2\cdot4}{3\cdot3}\right)\left(\frac{3\cdot5}{4\cdot4}\right)\left(\frac{4\cdot6}{5\cdot5}\right)\cdots\left(\frac{98\cdot100}{99\cdot99}\right)\left(\frac{99\cdot101}{100\cdot100}\right)
\]
A) $\frac{1}{25}$
B) $\frac{1}{50}$
C) $\frac{1}{100}$
D) $\frac{1}{200}$

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