
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
Rectangle $ABCD$ has an area of 24 square units. Points $E$ and $F$ are the midpoints of sides $AB$ and $CD$, respectively. Points $G$ and $H$ lie on side $AD$ and $BC$ respectively, such that $DG = 3 \cdot AG$ and $BH = 3 \cdot CH$. What is the area of triangle $AEG$?

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