
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
Triangle $DEF$ has vertices $D = (d_1, d_2)$, $E = (e_1, e_2)$, and $F = (f_1, f_2)$ in the first quadrant. These points are transformed using the reflection across the line $y = x$ followed by a 90-degree rotation clockwise. This sequence of transformations results in a new triangle $D'E'F'$. Determine if the following statements are always true:
1. Triangle $D'E'F'$ has its centroid in the first quadrant.
2. The areas of triangles $DEF$ and $D'E'F'$ are equal.
3. The slopes of lines $DD'$ and $FF'$ are the same.
A) Statements 1, 2, and 3 are true.
B) Only Statements 2 and 3 are true.
C) Only Statements 1 and 2 are true.
D) Only Statement 2 is true.
E) All statements are false.

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