
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 side as follows: $\triangle ABP$ and $\triangle ABQ$ are right triangles with $AB = BP = 8$ units and $AB = BQ = 5$ units. Let $E$ be the point on line segment $BQ$ such that $BE : EQ = 1:2$. Determine the area of $\triangle APE$.

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