
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
Given the set of numbers arranged according to a certain rule: $2^{100}, 2^{101}, 2^{102}, ..., 2^{199}, 2^{200}$, where $2^{100}$ is represented as $S$, express the sum of this set of data in terms of $S$.

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