
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 b and integer m define
\[{b \choose m} = \frac{b(b-1)(b-2)\cdots(b-(m-1))}{m(m-1)(m-2)\cdots(2)(1)}\]
What is \[{1 \choose 101} \div {-1 \choose 101}?\]
A) 0
B) 1
C) -1
D) 2
E) -2

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