
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 triangle $ABC$, let $E$ be a point on side $\overline{AC}$ such that $AE = \frac{1}{3}AC$ and $F$ be the midpoint of side $\overline{AB}$. The area of $\triangle ABC$ is 36 square units. What is the area of $\triangle AEF$?

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