
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 $|\vec{a}| = \sqrt{2}$ and $|\vec{b}| = 1$,
(1) If $\vec{a} \cdot \vec{b} = 1$, find the angle between $\vec{a}$ and $\vec{b}$.
(2) If the angle $\theta$ between $\vec{a}$ and $\vec{b}$ is 45°, find the value of $|\vec{a} - \vec{b}|$.

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