
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 
\[
{a \choose k} = \frac{a(a-1)(a-2)\cdots(a-(k-1))}{k(k-1)(k-2)\cdots(2)(1)}
\]
What is 
\[
{-\frac{1}{2} \choose 50} \div {\frac{1}{2} \choose 50}?
\]
A) -100  
B) -99  
C) 99  
D) -1  
E) 1

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