
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 non-zero vectors $\vec{a}$ and $\vec{b}$ satisfy: $2\vec{a} \cdot (2\vec{a} -\vec{b} )=\vec{b} \cdot (\vec{b} -2\vec{a} )$ and $|\vec{a} -\sqrt{2} \vec{b} |=3|\vec{a} |$, then the angle between $\vec{a}$ and $\vec{b}$ is ______.

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