
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 $n \in \mathbb{N}^*$, let the horizontal coordinate of the intersection point between the tangent line at point $(1,1)$ and the $x$-axis be denoted as $(x_n)$. Determine the value of ${x_1} \cdot {x_2} \cdot \cdots \cdot {x_n}$.

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