
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
Let $\mathbf{i}=(1,0)$, $\mathbf{j}=(0,1)$, $\mathbf{a}=2\mathbf{i}+3\mathbf{j}$, $\mathbf{b}=k\mathbf{i}-4\mathbf{j}$. If $\mathbf{a} \perp \mathbf{b}$, then the real number $k$ is $\boxed{6}$.

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