
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 curve $y = x^{n+1}$ where $n \in \mathbb{N}^*$, the tangent line at the point $(1,1)$ intersects the $x$-axis at the point with the $x$-coordinate $x_n$. Let $a_n = \lg x_n$, find the value of the sum $a_1 + a_2 + \cdots + a_{99}$.

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