
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
In triangle $ABC$, it is known that $AB = \sqrt{14}$ and $BC = 2$. A circle is drawn through point $B$, the midpoint $D$ of segment $BC$, and point $E$ on segment $AB$, and it is tangent to side $AC$. Find the ratio in which this circle divides segment $AB$ if $DE$ is the diameter of this circle.

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