
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 $|\vec{a}|=3$, $|\vec{b}|=4$, and the angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{3}$, find $\vec{a}\cdot\vec{b}$, $|\vec{a}-\vec{b}|$;  
(2) Given $|\vec{a}|=3$, $\vec{b}=(1,2)$, and $\vec{a}\parallel\vec{b}$, find the coordinates of $\vec{a}$.

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