
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
Let $x$ be a real number and $k$ be a nonnegative integer. Using the binomial coefficient definition,
\[
\binom{x}{k} = \frac{x(x-1)(x-2)...(x-k+1)}{k!},
\]
compute the value of
\[
\frac{\binom{1/2}{3} \cdot 4^3}{\binom{6}{3}}.
\]

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