
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
Examine the accuracy of the following approximate construction using a calculator. Let the circle $k$ have $AB$ as its diameter, with the second trisection point from $A$ being $C$ (i.e., $AC = 2CB$). Furthermore, let $D$ be one endpoint of the chord perpendicular to $AB$ at $C$, and let $E$ be the intersection point on line segment $AB$ of the circle centered at $A$ with radius $AD$. Then the segment $BE$ is approximately equal to the side length of a regular 17-sided polygon inscribed in circle $k$.

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