
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 a square $EFGH$ with a side length of 6 units. Inside this square, two smaller squares are drawn, each with side lengths as indicated, and a line segment is drawn across from vertex $E$ to vertex $G$. The smaller squares are situated such that their vertices touch $EF$, $GH$ and align with the midpoints of these sides. Label the side lengths of these squares as 2 and 3, respectively. Calculate the area of the region outside the squares but inside the triangle $\triangle EFG$.

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