
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
Let $\overline{AB}$ be a diameter in a circle with radius $6$. Let $\overline{CD}$ be a chord in the circle that intersects $\overline{AB}$ at point $E$ such that $BE = 3$ and $\angle AEC = 60^{\circ}$. Find the value of $CE^{2} + DE^{2}$.

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