
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 tangent line at the point (1, 1) on the curve $y = x^{n+1}$ (where $n \in \mathbb{Z}^*$) intersect the x-axis at the point with the x-coordinate $x_n$. Find the value of the product $x_1 \cdot x_2 \cdot x_3 \cdots x_n$.

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