
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
Calculate: 

\[
\frac{1}{2^{1998}}\left(1-3 C_{1998}^{2}+3^{2} C_{1998}^{4}-3^{3} C_{1998}^{6}+\cdots+3^{998} C_{1998}^{1996} -3^{999} C_{1998}^{1998} \right)
\]

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