
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
A circle is drawn through the vertices $A$ and $B$ of triangle $ABC$, intersecting sides $BC$ and $AC$ at points $D$ and $E$ respectively. The area of triangle $CDE$ is seven times smaller than the area of quadrilateral $ABDE$. Find the chord $DE$ and the radius of the circle, given $AB = 4$ and $\angle C = 45^\circ$.

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