
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 $|\overset{→}{a}| = 1$ and $|\overset{→}{b}| = \sqrt{2}$,

(I) If the angle between $\overset{→}{a}$ and $\overset{→}{b}$ is $60^{\circ}$, find $|\overset{→}{a} + \overset{→}{b}|$;

(II) If $\overset{→}{a} - \overset{→}{b}$ is perpendicular to $\overset{→}{a}$, find the angle between $\overset{→}{a}$ and $\overset{→}{b}$.

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