
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
Non-zero vectors $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are non-collinear vectors. Vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfy $\overrightarrow{a} = 2\overrightarrow{e_{1}} - \overrightarrow{e_{2}}$ and $\overrightarrow{b} = k\overrightarrow{e_{1}} + \overrightarrow{e_{2}}$. If $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear, then the value of the real number $k$ is \_\_\_\_\_\_.

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