
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 that $a$, $b$, and $c$ are positive numbers that are not all equal, evaluate the following statements:  
① $(a-b)^2+(b-c)^2+(c-a)^2 \neq 0$;  
② Among $a>b$, $a<b$, and $a=b$, at least one is true;  
③ It is impossible for $a \neq c$, $b \neq c$, and $a \neq b$ to all be true simultaneously.  
The correct judgments are __________.

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