
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 two non-zero planar vectors $\overrightarrow{a}, \overrightarrow{b}$ that satisfy the condition: for any $λ∈R$, $| \overrightarrow{a}-λ \overrightarrow{b}|≥slant | \overrightarrow{a}- \frac {1}{2} \overrightarrow{b}|$, then:
$(①)$ If $| \overrightarrow{b}|=4$, then $\overrightarrow{a}· \overrightarrow{b}=$ _______ ;
$(②)$ If the angle between $\overrightarrow{a}, \overrightarrow{b}$ is $\frac {π}{3}$, then the minimum value of $\frac {|2 \overrightarrow{a}-t· \overrightarrow{b}|}{| \overrightarrow{b}|}$ is _______ .

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