
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
For any real number \( a \) and positive integer \( k \), define
\[ {a \choose k} = \frac{a(a-1)(a-2)\cdots(a-(k-1))}{k(k-1)(k-2)\cdots(2)(1)} \]
Evaluate:
\[ {-\frac{3}{4} \choose 100} \div {\frac{3}{4} \choose 100} \]
**A)** \(-199\)  
**B)** \(-1\)  
**C)** \(1\)  
**D)** \(197\)  
**E)** \(199\)

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