
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
Triangles \( ABC \) and \( ADE \) are such that \( B \) is the midpoint of \( \overline{DE} \). Also, \( AB = DE = 2 \), \( BC = 8 \), \( CA = \sqrt{72} \), and
\[
\overrightarrow{AB} \cdot \overrightarrow{AD} + \overrightarrow{AC} \cdot \overrightarrow{AE} = 5.
\]
Find the cosine of the angle between vectors \( \overrightarrow{DE} \) and \( \overrightarrow{BC} \).

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