
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
In the Cartesian coordinate system, the coordinates of $P_1$ are (1, 0). Rotate it counterclockwise around the origin by 30° to get point $P_2$. Extend $OP_2$ to point $P_3$ such that $OP_3 = 2OP_2$. Then, rotate point $P_3$ counterclockwise around the origin by 30° to get $P_4$. Extend $OP_4$ to point $P_5$ such that $OP_5 = 2OP_4$. Continue this process, then the coordinates of point $P_{2010}$ are.

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