
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
Let $a$, $b$, $c$ be vectors. Among the following statements, the correct one is:

① If $a \cdot b = b \cdot c$, then $a = c$;  
② $(a \cdot b) \cdot c = a \cdot (b \cdot c)$;  
③ $|a \cdot b| = |a| \cdot |b|$;  
④ $|a+b|^2 = (a+b)^2$;  
⑤ If $a \parallel b$ and $b \parallel c$, then $a \parallel c$;  
⑥ If $a \perp b$ and $b \perp c$, then $a \perp c$.

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