
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 rectangle $ABCD$, $AB = 4$ and $BC = 10$. The rectangle is folded along a line through $A$ such that point $A$ meets side $CD$ at point $G$, where $DG = 3$. After the fold, point $C$ touches the extension of side $AB$ at point $E$. Calculate the length of segment $CE$. Express your answer in simplest radical form.

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