
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 \( R \) be the set of all possible remainders when a number of the form \( 2^n \), \( n \) a nonnegative integer, is divided by 2000. Let \( S \) be the sum of the elements in \( R \). Find the remainder when \( S \) is divided by 2000.

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