
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 non-zero vectors $\overrightarrow{a}$ and $\overrightarrow{b}$, if $|\overrightarrow{a}| = |\overrightarrow{b}| = 1$ and $\overrightarrow{a} \perp \overrightarrow{b}$, and $(2\overrightarrow{a} + 3\overrightarrow{b}) \perp (k\overrightarrow{a} - 4\overrightarrow{b})$, then the value of the real number $k$ is _______.

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