
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 following product:
\[
\left(\frac{1\cdot3}{2\cdot3}\right)\left(\frac{2\cdot4}{3\cdot4}\right)\left(\frac{3\cdot5}{4\cdot5}\right)\cdots\left(\frac{99\cdot101}{100\cdot101}\right)\left(\frac{100\cdot102}{101\cdot102}\right)\cdot \left(\frac{103}{101}\right)
\]
**A)** $\frac{103}{102}$  
**B)** $\frac{103}{10201}$  
**C)** $\frac{100}{10001}$  
**D)** $\frac{100}{102}$

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