
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 $|\vec{a}|=2$, $|\vec{b}|=1$, and the angle between $\vec{a}$ and $\vec{b}$ is 60°, find $|2\vec{a} - \vec{b}|$;  
(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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