
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 a plane that satisfy the conditions $| \overset{→}{a}|= \sqrt{2},| \overset{→}{b}|=2, (\overset{→}{a}- \overset{→}{b})⊥ \overset{→}{a} $,

(1) Find the angle between $ \overset{→}{a} $ and $ \overset{→}{b} $;

(2) Calculate $|2 \overset{→}{a}+ \overset{→}{b}|$.

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