
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
In the Cartesian coordinate system $xOy$, given vectors $\overrightarrow{a} = (1, 0)$, $\overrightarrow{b} = (0, 1)$. If the vector $2\overrightarrow{a} - 3\overrightarrow{b}$ is collinear with the vector $k\overrightarrow{a} + 6\overrightarrow{b}$, then the value of the real number $k$ is \_\_\_\_\_\_.

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