
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 $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are two unit vectors with an angle of $\dfrac {2}{3}π$ between them, $\overrightarrow{a}= \overrightarrow{e_{1}}-2 \overrightarrow{e_{2}}$, and $\overrightarrow{b}=k \overrightarrow{e_{1}}+ \overrightarrow{e_{2}}$, find the value of the real number $k$ such that $\overrightarrow{a} \cdot \overrightarrow{b}=0$.

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