
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 vectors $\overrightarrow{a} = (\sqrt{3}, 1)$, $\overrightarrow{b} = (0, -1)$, $\overrightarrow{c} = (k, \sqrt{3})$, if $\overrightarrow{a} + 2\overrightarrow{b}$ is collinear with $\overrightarrow{c}$, then $k = \_\_\_\_\_\_$.

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