
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
A right-angled triangle, with vertices at points A (0,0), B (1,0), and C (0,1), is first rotated $180^\circ$ counterclockwise around the origin, then reflected across the x-axis, followed by a translation 2 units to the right. Determine the final coordinates of the triangle.
A) $(2,0), (1,0), (2,-1)$
B) $(2,0), (1,0), (2,1)$
C) $(0,2), (-1,2), (0,1)$
D) $(0,0), (-1,0), (0,1)$

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