
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 the following pairs of coordinates, identify the values of \(x\) and \(y\) for each pair:
1. \((x_{1}, y_{1}) = \left( \frac{4\pi}{5}, -\frac{\pi}{5} \right)\)
2. \((x_{2}, y_{2}) = \left( \frac{12\pi}{5}, -\frac{3\pi}{5} \right)\)
3. \((x_{3}, y_{3}) = \left( \frac{4\pi}{3}, -\frac{\pi}{3} \right)\)

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