
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 $\overset{→}{a}$ and $\overset{→}{b}$ are two non-zero vectors, and $(\overset{→}{a} - 2\overset{→}{b}) \perp \overset{→}{a}, (\overset{→}{b} - 2\overset{→}{a}) \perp \overset{→}{b}$, find the angle between vector $\overset{→}{a}$ and vector $\overset{→}{b}$ ($\theta$).

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