
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 $\mathbf{i} = (1, 0)$, $\mathbf{j} = (0, 1)$, $\mathbf{a} = 2\mathbf{i} + 3\mathbf{j}$, and $\mathbf{b} = k\mathbf{i} - 4\mathbf{j}$. If $\mathbf{a}$ is perpendicular to $\mathbf{b}$, calculate the value of the real number $k$.

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