
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
How many of the five tetrominoes shown below have at least one rotational symmetry of 90 degrees or 180 degrees, and how many distinct tetrominoes are there when considering all rotations and reflections?
[asy]
unitsize(0.5cm);
filldraw(shift(1,1)*unitsquare);
filldraw(shift(1,2)*unitsquare);
filldraw(shift(1,3)*unitsquare);
filldraw(shift(2,3)*unitsquare); // L-shaped

filldraw(shift(5,1)*unitsquare);
filldraw(shift(5,2)*unitsquare);
filldraw(shift(6,1)*unitsquare);
filldraw(shift(6,2)*unitsquare); // Square

filldraw(shift(9,1)*unitsquare);
filldraw(shift(9,2)*unitsquare);
filldraw(shift(9,3)*unitsquare);
filldraw(shift(10,2)*unitsquare); // T-shaped

filldraw(shift(13,1)*unitsquare);
filldraw(shift(13,2)*unitsquare);
filldraw(shift(14,1)*unitsquare);
filldraw(shift(14,2)*unitsquare); // Square (same as second)

filldraw(shift(17,1)*unitsquare);
filldraw(shift(17,2)*unitsquare);
filldraw(shift(18,1)*unitsquare);
filldraw(shift(18,2)*unitsquare); // Square (same as second and fourth)
[/asy]
A) 2, 2
B) 3, 2
C) 2, 3
D) 3, 3
E) 4, 3

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