
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 that for any planar vector $\overrightarrow {AB} = (x, y)$, rotating $\overrightarrow {AB}$ counterclockwise around its starting point by an angle $\theta$ to get vector $\overrightarrow {AP} = (x\cos\theta - y\sin\theta, x\sin\theta + y\cos\theta)$ is called rotating point B around point A counterclockwise by an angle $\theta$ to get point P. It is known that in the plane, point A is at (1, 2), and point B is at $(1+ \sqrt {2}, 2-2 \sqrt {2})$; if point B is rotated clockwise around point A by $\frac {\pi}{4}$ to get point P, then the coordinates of point P are \_\_\_\_\_\_.

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