
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
Consider three right triangles arranged as follows: Triangle $ABC$ with $AB = 8$ (base) and $BC = 12$ (height); Triangle $CBD$ with $BD = 8$ (height); Triangle $BEF$ with $EF = 4$ (base) and $BF = 8$ (height). Points lie such that $C$ is directly above $B$, $D$ is directly above $B$, and $F$ is directly above $B$. Calculate the area of triangle $AEF$ where $E$ is the midpoint of $BD$.

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