
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
The integer part of the value of the expression \( 10 \cdot 75 \cdot \left(1+\frac{1}{1 \cdot 3}\right)\left(1+\frac{1}{2 \cdot 4}\right)\left(1+\frac{1}{3 \cdot 5}\right)\left(1+\frac{1}{4 \cdot 6}\right) \cdots \left(1+\frac{1}{98 \cdot 100}\right)\left(1+\frac{1}{99 \cdot 101}\right) \) can be found by evaluating the product and then determining the integer part of the result.

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