
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 \(ABC\), the median \(BM\) is drawn. \(MD\) and \(ME\) are the angle bisectors of triangles \(AMB\) and \(CMB\) respectively. Segments \(BM\) and \(DE\) intersect at point \(P\), with \(BP = 1\) and \(MP = 3\).

a) Find the length of segment \(DE\).

b) Given that a circle can be circumscribed around quadrilateral \(ADEC\), find its radius.

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