
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
Let $T'$ be the triangle in the coordinate plane with vertices $(0,0), (6,0),$ and $(0,4)$. Consider the following transformations of the plane: rotations of $90^\circ, 180^\circ,$ and $270^\circ$ counterclockwise around the origin, reflection across the $x$-axis, reflection across the $y$-axis, and reflection across the line $y = x$. How many of the $216$ sequences of three of these transformations will return $T'$ to its original position?
A) 15
B) 20
C) 24
D) 25
E) 30

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