
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
In $\triangle ABC$, $AB=1$, $BC=2$, $\angle B= \frac {\pi}{3}$, let $\overrightarrow{AB}= \overrightarrow{a}$, $\overrightarrow{BC}= \overrightarrow{b}$
(I) Find the value of $(2 \overrightarrow{a}-3 \overrightarrow{b}) \cdot (4 \overrightarrow{a}+ \overrightarrow{b})$;
(II) Find the value of $|2 \overrightarrow{a}- \overrightarrow{b}|$.

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