
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 movement pattern of A: first move vertically upwards by 1 unit length, then move horizontally to the right by 2 unit lengths; the movement pattern of B: first move vertically downwards by 2 unit lengths, then move horizontally to the left by 3 unit lengths. In the Cartesian coordinate system, there is a moving point P that starts from the origin O and moves to point P<sub>1</sub> according to A's movement pattern for the first time, then moves from point P<sub>1</sub> to point P<sub>2</sub> according to B's movement pattern for the second time, then moves from point P<sub>2</sub> to point P<sub>3</sub> according to A's movement pattern for the third time, then moves from point P<sub>3</sub> to point P<sub>4</sub> according to B's movement pattern for the fourth time, and so on, following this pattern of movement. After the 15th movement, the coordinates of the position P<sub>15</sub> where the moving point P is located are.

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