
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 that \( P_{0}(1, f(1)) \) is a point on the curve \( C: f(x) = \mathrm{e}^{x} \), the tangent line \( l_{1} \) to \( C \) at \( P_{0} \) intersects the \( x \)-axis at point \( Q_{1}(x_{1}, 0) \). A vertical line through \( Q_{1} \) intersects \( C \) at \( P_{1} \), and the tangent line \( l_{2} \) to \( C \) at \( P_{1} \) intersects the \( x \)-axis at \( Q_{2}(x_{2}, 0) \). A vertical line through \( Q_{2} \) intersects \( C \) at \( P_{2} \), and the tangent line \( l_{3} \) to \( C \) at \( P_{2} \) intersects the \( x \)-axis at \( Q_{3}(x_{3}, 0) \). By repeating this operation, points \( Q_{4}(x_{4}, 0), Q_{5}(x_{5}, 0), \cdots \) are obtained in succession. Find \( x_{2023} \).

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