
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 $\overrightarrow{a}=(2,k)$ and $\overrightarrow{b}=(1,1)$, where $\overrightarrow{b} \perp (\overrightarrow{a} - 3\overrightarrow{b})$.

1. Find the value of $k$.
2. Find the cosine value of the angle between vectors $\overrightarrow{a}$ and $\overrightarrow{b}$.

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