
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 vectors $ \vec{a} $ and $ \vec{b} $ satisfy $| \vec{a}|=| \vec{b}|=2 $, and $ \vec{b} \perp (2 \vec{a}+ \vec{b}) $, calculate the angle between vector $ \vec{a} $ and $ \vec{b} $.

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