
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 $\overrightarrow{a}$ and $\overrightarrow{b}$ are two unit vectors.  
(I) If $|\overrightarrow{a} - 2\overrightarrow{b}| = 2$, find the value of $|\overrightarrow{a} - \overrightarrow{b}|$;  
(II) If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is 60°, find the cosine of the angle between vector $\overrightarrow{m} = \overrightarrow{a} + \overrightarrow{b}$ and $\overrightarrow{n} = \overrightarrow{a} - 3\overrightarrow{b}$.

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