
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 $C$ be a point not on line $AE$. Points $D$ and $F$ lie on line $AE$ such that $CD \perp AE$ and $CF \perp AE$. Meanwhile, $B$ is a point on line $CE$ such that $AB \perp CE$. Given $AB = 3$, $CD = 10$, and $AE = 6$, find the lengths of $CE$ and $CF$.

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