
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 \(ABC\), a 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 \(BP = 2\) and \(MP = 4\).

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

b) Additionally, it is known 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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