
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
In an isosceles triangle $ABC$ with $AB = AC = 10$ and $BC = 12$, four distinct points $D_1, D_2, E_1, E_2$ are located such that the triangles $AD_1E_1$, $AD_1E_2$, $AD_2E_1$, and $AD_2E_2$ are each congruent to triangle $ABC$, with $BD_1 = BD_2 = 5$. Calculate $\sum (CE_k)^2$ for $k = 1, 2$.

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