
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 vector $\overset{→}{a} \cdot(\overset{→}{a} +2 \overset{→}{b} )=0$, $| \overset{→}{a} |=2$, $| \overset{→}{b} |=2$, find the angle between vectors $\overset{→}{a}$ and $\overset{→}{b}$.

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