
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
On a plane, five points $A, B, C, D, E$ satisfy the following conditions: $A B = 16$ cm, $B C = 8$ cm, $A D = 10$ cm, $D E = 2$ cm, $A C = 24$ cm, and $A E = 12$ cm. If the area of triangle $E A B$ is 96 square centimeters, what is the distance from point $A$ to line $CD$ in centimeters?

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