
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 $e\_1$ and $e\_2$ are two non-zero non-collinear vectors, $a = 2e\_1 - e\_2$, and $b = ke\_1 + e\_2$ ($k \in \mathbb{R}$), if $a$ and $b$ are collinear vectors, find the value of the real number $k$.

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