
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 $y=x^{n+1}$ ($n\in\mathbb{N}^*$) and the horizontal coordinate of the intersection point of its tangent line at point $(1,1)$ with the x-axis is $x_n$. Let $a_n=\log_ {10}x_n$, find the value of $a_1+a_2+a_3+...+a_{999}$.

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