
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 two unit vectors $\overrightarrow {e_{1}}$ and $\overrightarrow {e_{2}}$ with an angle of $\frac {2}{3}\pi$ between them, and $\overrightarrow {a}= \overrightarrow {e_{1}}-2 \overrightarrow {e_{2}}$, $\overrightarrow {b}=k \overrightarrow {e_{1}}+ \overrightarrow {e_{2}}$. If $\overrightarrow {a}$ is perpendicular to $\overrightarrow {b}$, then find the value of $k$. (Jiangsu 2011)

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