
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 five isometries of the plane: rotations of \( 90^\circ, 180^\circ, \) and \( 270^\circ \) counterclockwise around the origin, reflection across the \( x \)-axis, and reflection across the \( y \)-axis. How many of the 125 sequences of three of these transformations (not necessarily distinct) will return \( T \) to its original position?
A) 14
B) 16
C) 18
D) 20
E) 24

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