
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 \( n = 1990 \), then
$$
\begin{aligned}
& \frac{1}{2^{n}}\left(1-3 \binom{n}{2}+3^{2} \binom{n}{4}-3^{3} \binom{n}{6}+\cdots+3^{994} \binom{n}{1988}-3^{995} \binom{n}{1990}\right) \\
= &
\end{aligned}
$$

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