
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 $Q$ be the quadrilateral in the coordinate plane with vertices at $(0,0), (6,0), (6,4),$ and $(0,4)$. Consider the following six isometries (rigid 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 (not necessarily distinct) will return $Q$ to its original position?
A) 16
B) 18
C) 20
D) 22
E) 24

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