
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
A particle moves in the plane along the direction $\overrightarrow {u}=(1,2)$. It is desired to set a line $l$ in this plane so that when the particle hits line $l$, it reflects according to the optical principle (the angle of incidence equals the angle of reflection) and then moves along the direction $\overrightarrow {v}=(-2,1)$. One of the direction vectors of line $l$, $\overrightarrow {\omega }$, is __________.

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