
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
Let $\overrightarrow {e_{1}}$ and $\overrightarrow {e_{2}}$ be two non-collinear vectors in a plane, $\overrightarrow {AB}=(a-1) \overrightarrow {e_{1}}+ \overrightarrow {e_{2}}$, $\overrightarrow {AC}=b \overrightarrow {e_{1}}-2 \overrightarrow {e_{2}}$, with $a>0$, $b>0$. If points A, B, and C are collinear, then the minimum value of $\frac {1}{a}+ \frac {2}{b}$ is \_\_\_\_\_\_.

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