
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 a sequence $\{x_n\}$ that satisfies $\lg x_{n+1} = 1 + \lg x_{n}$ ($n \in N^{*}$), and $x_1 + x_2 + x_3 + \ldots + x_{100} = 1$, find the value of $\lg (x_{101} + x_{102} + \ldots + x_{200})$.

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