
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
(1) Given that $| \overrightarrow{a}|=2$, $| \overrightarrow{b}|=1$, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $60^{\circ}$, find $|2 \overrightarrow{a}- \overrightarrow{b}|$;
(2) If $\tan \theta=3$, find the value of $\frac {5\sin ^{3}\theta+\cos \theta}{2\cos ^{3}\theta +\sin ^{2}\theta \cos \theta }$.

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