
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
Calculate the value of the product: $\left(\frac{1\cdot5}{3\cdot3}\right)\left(\frac{3\cdot7}{5\cdot5}\right)\left(\frac{5\cdot9}{7\cdot7}\right)\cdots\left(\frac{95\cdot99}{97\cdot97}\right)\left(\frac{97\cdot101}{99\cdot99}\right)$.

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