
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
Quadrilateral $ABCD$ is structured such that $AB = 7$ units, $BC = 6$ units, and $CD = 21$ units. Angles $B$ and $C$ are both right angles. From vertex $C$, extend a line segment $CE$ perpendicular to $CD$ with length $CE = 10$ units. Compute the length of segment $AD$.

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