
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
There are five points $A$, $B$, $C$, $D$, and $E$ on the plane satisfying: $AB = 8$ cm, $BC = 4$ cm, $AD = 5$ cm, $DE = 1$ cm, $AC = 12$ cm, and $AE = 6$ cm. If the area of triangle $EAB$ is 24 square cm, find the distance from point $A$ to line $CD$.

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