
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 that the sequence $\{ \log_2 x_n \}$ is an arithmetic sequence with a common difference of $1$, and the sum of the first 100 terms of the sequence $\{ x_n \}$ is equal to $100$, the sum of the first 200 terms of the sequence $\{ x_n \}$ is equal to which of the following?
A) $100 \times (1 + 2^{100})$
B) $100 \times 2^{100}$
C) $1 + 2^{100}$
D) $200$

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