
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 any two non-zero planar vectors $\overrightarrow {α}$ and $\overrightarrow {β}$, define $\overrightarrow {αβ}$ = $\frac { \overrightarrow {α}\cdot \overrightarrow {β}}{ \overrightarrow {β}\cdot \overrightarrow {β}}$. If the planar vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ satisfy $|\overrightarrow {a}|≥|\overrightarrow {b}|>0$, the angle θ between $\overrightarrow {a}$ and $\overrightarrow {b}$ is in the interval (0, $\frac {π}{6}$), and both $\overrightarrow {ab}$ and $\overrightarrow {ba}$ are in the set {$\frac {n}{3}$|n∈Z}, calculate $\overrightarrow {ab}$.

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