
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 vectors $\overset{→}{a}$ and $\overset{→}{b}$ in the plane that satisfy $|\overset{→}{a}| = 2$ and $(2\overset{→}{a} + \overset{→}{b}) \cdot \overset{→}{b} = 12$, find the range of values for $|\overset{→}{b}|$.

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