
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 $\overset{→}{a}=(1,1)$ and $\overset{→}{b}=(0,−2)$, determine the value(s) of $k$ for which:

1. $k\overset{→}{a}−\overset{→}{b}$ is collinear with $\overset{→}{a}+\overset{→}{b}$
2. The angle between $k\overset{→}{a}−\overset{→}{b}$ and $\overset{→}{a}+\overset{→}{b}$ is ${120}^{∘}$

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