
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
Point \( C \) moves along a line segment \( AB \) of length 4. There are two isosceles triangles \( ACD \) and \( BEC \) on the same side of the line passing through \( AB \) such that \( AD = DC \) and \( CE = EB \). Find the minimum length of segment \( DE \).

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