
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 $\overline{a} = (-3, 1)$ and $\overline{b} = (1, -2)$, if $(-2\overline{a} + \overline{b})$ is parallel to $(\overline{a} + k\overline{b})$, determine the value of the real number $k$.

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