
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 $\overrightarrow{a}$, $\overrightarrow{b}$, $\overrightarrow{c}$, among the following statements, the correct one is __________.  
① If $\overrightarrow{a}\parallel \overrightarrow{b}$, $\overrightarrow{b}\parallel \overrightarrow{c}$, 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 $\overrightarrow{a}\perp \overrightarrow{b}$, $\overrightarrow{b}\perp \overrightarrow{c}$, then $\overrightarrow{a}\perp \overrightarrow{c}$.

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