
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 of radius $10$. Let $\overline{CD}$ be another chord that intersects $\overline{AB}$ at a point $E$ such that $BE=5$, and $\angle AEC = 60^\circ$. What is the value of $CE^2 + DE^2?$
A) 90
B) 95
C) 100
D) 105

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