
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
Equilateral triangle $ABC$ has side length 10. There are two distinct triangles $AD_1E_1$ and $AD_2E_2$, each congruent to triangle $ABC$, with $BD_1 = BD_2 = 3$. Find $(CE_1)^2 + (CE_2)^2$.

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