
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 a 6 units by 8 units rectangle, triangle $DEF$ has vertices $D$, $E$, and $F$ on the sides of the rectangle such that $D$ is at the midpoint of the shorter side, $E$ is at the bottom right corner, and $F$ is on the longer side, 3 units from the top right corner. Another triangle $GHI$ shares vertex $I$ with vertex $F$ of triangle $DEF$, vertex $G$ is the top left corner of the rectangle and vertex $H$ is on the longer side, 2 units from the top left corner. Calculate the areas of triangles $DEF$ and $GHI$ in square units.

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