
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 the curve $y=x^{n+1}$ $(n\in N^*)$ have a tangent at the point $(1,1)$, and let the x-coordinate of the intersection of this tangent with the x-axis be $x_n$. Let $a_n=\lg x_n$, then the value of $a_1+a_2+a_3+...+a_{99}$ is

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