
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 not collinear, if $(\vec{a} + k\vec{b}) \perp (\vec{a} - k\vec{b})$, then $k =$ __.

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