
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
In a right triangle ABC with a right angle at A, let AB = 8 units and AC = 12 units. A triangle ABD is formed by extending side AB to point D such that BD = 8 units and D lies on the same line as AB. A point E divides AD externally in the ratio 1:3, meaning AE : ED = 1:3. Find the area of triangle ACE.

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