
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
The real number sequence \( x_0, x_1, x_2, \cdots \), is defined as \( x_0 = 1989 \) and \( x_n = -\frac{1989}{n} \sum_{k=0}^{n-1} x_k \) for \( n \geq 1 \). Calculate the value of \( \sum_{n=0}^{1988} 2^n x_n \).

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