
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
If $x$ is a real number and $k$ is a nonnegative integer, the binomial coefficient $\binom{x}{k}$ is defined as 
\[
  \binom{x}{k} = \frac{x(x - 1)(x - 2) \dots (x - k + 1)}{k!}.
\]
Compute the value of
\[
  \frac{\binom{-1/2}{1007} \cdot 3^{1007}}{\binom{2014}{1007}}.
\]

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