
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 $\overrightarrow {a}$ and $\overrightarrow {b}$ that are not collinear, $\overrightarrow {c}$ = k$\overrightarrow {a}$ + $\overrightarrow {b}$, and $\overrightarrow {d}$ = $\overrightarrow {a}$ - $\overrightarrow {b}$:

1. If $\overrightarrow {c}$ is parallel to $\overrightarrow {d}$, find the value of k and determine whether $\overrightarrow {c}$ and $\overrightarrow {d}$ have the same direction.
2. If $|\overrightarrow {a}| = |\overrightarrow {b}|$ and the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ is 60°, find the value of k that makes $\overrightarrow {c}$ perpendicular to $\overrightarrow {d}$.

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