
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 $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ be unit vectors forming an angle of $\frac{2\pi}{3}$ with each other, and let $\overrightarrow{a}=2\overrightarrow{e_{1}}+3\overrightarrow{e_{2}}$, $\overrightarrow{b}=k\overrightarrow{e_{1}}-4\overrightarrow{e_{2}}$. If $\overrightarrow{a}$ is perpendicular to $\overrightarrow{b}$, determine the value of the real number $k$.

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