
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 two tangent circles $k$ and $k_{1}$ with a radius of one unit each in a plane. One of their common external tangents is the line $e$. Subsequently, we draw circles $k_{2}, k_{3}, \ldots, k_{n}$ such that each of them is tangent to $k$, $e$, and the circle with a sequence number one less than its own. What is the radius of the circle $k_{n}$?

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