
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 that the angle between non-zero vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ is $\frac {2π}{3}$, and $|\overrightarrow {a}|=|\overrightarrow {a}+\overrightarrow {b}|$, find the minimum value of $\frac {|2 \overrightarrow {a}+t \overrightarrow {b}|}{|2 \overrightarrow {b}|}$.

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