
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
Given a triangle ABC defined in the coordinate plane with vertices at A(0,0), B(3,0), C(0,4), three transformations are defined:
- **T1**, a rotation by $90^\circ$ counterclockwise around the origin;
- **T2**, a reflection across the x-axis;
- **T3**, a reflection across the y-axis.
How many sequences of 12 transformations, chosen from {T1, T2, T3}, will return all the labeled vertices to their original positions?
**A) 12**  
**B) 20**  
**C) 24**  
**D) 28**  
**E) 30**

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