
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 $y$ is a fraction and $m$ is a nonnegative integer, recall that the binomial coefficient $\binom{y}{m}$ is defined by:
\[
  \binom{y}{m} = \frac{y(y - 1)(y - 2) \dots (y - m + 1)}{m!} \, .
\]
Compute the value of:
\[
  \frac{\binom{1/3}{1000} \cdot 9^{1000}}{\binom{2000}{1000}} \, .
\]

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