
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: \( AB = 8 \) cm, \( BC = 4 \) cm, \( AD = 5 \) cm, \( DE = 1 \) cm, \( AC = 12 \) cm, \( AE = 6 \) cm. If the area of triangle \( EAB \) is 24 square centimeters, what is the distance from point \( A \) to line \( CD \) in meters?

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