
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 $\mathbf{a}$ and $\mathbf{b}$ are two non-collinear unit vectors, and $k$ is a real number. If the vector $\mathbf{a} + \mathbf{b}$ is perpendicular to the vector $k\mathbf{a} - \mathbf{b}$, then $k = \boxed{\_\_\_\_\_\_\_\_}$.

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