
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
Two right triangles share a hypotenuse as follows: Triangle ABC and Triangle DBC are right-angled at C and D respectively. AC = 8 units, BC = 6 units, and CD = 2 units. Point E lies on segment AD such that AE:ED = 2:1. What is the area of Triangle AEC?

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