
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 the generalized binomial coefficient defined for any real number \(a\) and positive integer \(k\) as \({a \choose k} = \frac{a(a-1)...(a-(k-1))}{k!}\), compute \({-\frac{3}{2} \choose 50} \cdot {\frac{3}{2} \choose 50}\).
A) \(4^{-50} \cdot 43!^2 \cdot 50!\)
B) \(4^{-50} \cdot 43!^2 \cdot 51!\)
C) \(4^{-49} \cdot 43!^2 \cdot 51!\)
D) \(4^{-50} \cdot 44!^2 \cdot 50!\)

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