
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 $|\vec{a}|=2$, $|\vec{b}|=3$, and the angle between $\vec{a}$ and $\vec{b}$ is $60^{\circ}$, $\vec{c}=12\vec{a}+3\vec{b}$, $\vec{d}=3\vec{a}+k\vec{b}$. For what value of the real number $k$ does (1) $\vec{c}\parallel \vec{d}$ and (2) $\vec{c}\perp \vec{d}$?

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