
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 $ABC$, point $E$ divides side $\overline{AC}$ in a ratio of 1:2, where $E$ is closer to $A$, and $F$ is the midpoint of side $\overline{AB}$. If the area of $\triangle ABC$ is 36 square units, what is the area of $\triangle CEF$?

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