
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 distinct positive numbers, determine the validity of the following statements:

1. $(a - b)^2 + (b - c)^2 + (c - a)^2 \neq 0$;
2. At least one of the following is true: $a > b$, $a < b$, or $a = b$;
3. It is not possible for all of the following to be true simultaneously: $a \neq c$, $b \neq c$, $a \neq b$.

Indicate which of the above statements are correct.

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