
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 two vectors $\overrightarrow {a} = (\cos\alpha, \sin\alpha)$ and $\overrightarrow {b} = (\cos\beta, \sin\beta)$, and $\alpha - \beta = k\pi$ where $k \in \mathbb{Z}$, which of the following statements are true: 
① The angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ is equal to $\alpha - \beta$;
② The magnitudes of $\overrightarrow {a}$ and $\overrightarrow {b}$ are equal, $|\overrightarrow {a}| = |\overrightarrow {b}|$;
③ $\overrightarrow {a}$ is parallel to $\overrightarrow {b}$, $\overrightarrow {a} \parallel \overrightarrow {b}$;
④ $\overrightarrow {a}$ is orthogonal to $\overrightarrow {b}$, $\overrightarrow {a} \perp \overrightarrow {b}$.

Which conclusion numbers are correct?

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