
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
A sequence of real numbers  $ x_0, x_1, x_2, \ldots$  is defined as follows:  $ x_0 \equal{} 1989$  and for each  $ n \geq 1$ 

\[ x_n \equal{} \minus{} \frac{1989}{n} \sum^{n\minus{}1}_{k\equal{}0} x_k.\]

Calculate the value of  $ \sum^{1989}_{n\equal{}0} 2^n x_n.$ 

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