
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 $\overrightarrow {a}$, $\overrightarrow {b}$, $\overrightarrow {c}$, identify the correct statement(s) among the following:
① If $\overrightarrow {a}\parallel \overrightarrow {b}$ and $\overrightarrow {b}\parallel \overrightarrow {c}$, then $\overrightarrow {a}\parallel \overrightarrow {c}$.
② $|\overrightarrow {a} \cdot \overrightarrow {b}| = |\overrightarrow {a}| \cdot |\overrightarrow {b}|$.
③ $(\overrightarrow {a} \cdot \overrightarrow {b}) \cdot \overrightarrow {c} = \overrightarrow {a} \cdot (\overrightarrow {b} \cdot \overrightarrow {c})$.
④ If $\overrightarrow {a} \cdot \overrightarrow {b} = \overrightarrow {b} \cdot \overrightarrow {c}$, then $\overrightarrow {a} = \overrightarrow {c}$.
⑤ $|\overrightarrow {a} + \overrightarrow {b}|^2 = (\overrightarrow {a} + \overrightarrow {b})^2$.
⑥ If $\overrightarrow {a} \perp \overrightarrow {b}$ and $\overrightarrow {b} \perp \overrightarrow {c}$, then $\overrightarrow {a} \perp \overrightarrow {c}$.

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