
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 triangle with vertices at points \(A (1, 2)\), \(B (4, 2)\), and \(C (1, 5)\) is first rotated \(90^\circ\) clockwise around the origin, then reflected over the \(x\)-axis, followed by a translation 3 units up, and finally rotated \(180^\circ\) around the origin. Determine the final coordinates of the vertices of the triangle.

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