
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 $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfying $\overrightarrow{b}= \sqrt{2}$, and $(\overrightarrow{a}- \overrightarrow{b})\cdot(\overrightarrow{a}+ \overrightarrow{b})= \frac{1}{4}$.

(I) Find $|\overrightarrow{a}|$;

(II) When $\overrightarrow{a}\cdot \overrightarrow{b}=\frac{3}{2}$, find the value of the angle $\theta$ between $\overrightarrow{a}$ and $\overrightarrow{b}$.

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