
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 $\overrightarrow {OA} = (1, -2)$, $\overrightarrow {OB} = (a, -1)$, $\overrightarrow {OC} = (-b, 0)$ (where $a > 0$, $b > 0$, and $O$ is the origin of coordinates), and points A, B, C are collinear, calculate the minimum value of $\frac {2}{a} + \frac {1}{b}$.

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