
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 that $| \vec{a}|=3,$ $| \vec{b}|=4 $, and $| \vec{a}|$ and $| \vec{b}|$ are non-collinear planar vectors.

(1) If $(\vec{a}+k \vec{b}) \perp (\vec{a}-k \vec{b})$, find the value of $k$;

(2) If $(k \vec{a}-4 \vec{b}) \parallel (\vec{a}-k \vec{b})$, find the value of $k$.

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