
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 the diagram, square $PQRS$ has an area of $64 \text{ cm}^2$. Each side of square $PQRS$ has smaller squares positioned at its corners, each with sides 2 cm long. In triangle $DEF$, $DE = EF$, and when triangle $DEF$ is folded over side $\overline{EF}$, point $D$ coincides with $T$, which is a midpoint of edge $PQ$ of square $PQRS$. Determine the area of triangle $DEF$ in square centimeters, expressing your answer as a common fraction.

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