
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
Ant Borya moves on the coordinate plane, starting from the point \( P_{0} = (0, 0) \), moving to the point \( P_{1} = (1, 0) \), and then spiraling counterclockwise. Points with integer coordinates, which he reaches, form a sequence \( P_{n} \). Find the coordinates of the point \( P_{1557} \).

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