
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 $\overrightarrow {a}=(3,2)$, $\overrightarrow {b}=(-2,-4)$, and $\overrightarrow {c}= \overrightarrow {a}+k \overrightarrow {b}$, where $k \in \mathbb{R}$:
1. Find the value of $k$ if $\overrightarrow {b} \perp \overrightarrow {c}$.
2. Find the cosine value of the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$.

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