
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 \(ABC\) with angle \(A\) equal to \(60^\circ\), a bisector \(AD\) is drawn. The radius of the circumcircle of triangle \(ADC\) with its center at point \(D\) is \( \frac{2\sqrt{3}}{3} \). Find the length of segment \(BM\), where \(M\) is the intersection point of segments \(AD\) and \(BO\), if \(AB=1\).

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