
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
For non-zero real numbers $a$, $b$, $c$,  
① If $a$, $b$, $c$ form an arithmetic sequence, then $\frac {1}{a}$, $\frac {1}{b}$, $\frac {1}{c}$ also definitely form an arithmetic sequence;  
② If $a$, $b$, $c$ form an arithmetic sequence, then $a^2$, $b^2$, $c^2$ also definitely form an arithmetic sequence;  
③ If $a$, $b$, $c$ form a geometric sequence, then $\frac {1}{a}$, $\frac {1}{b}$, $\frac {1}{c}$ also definitely form a geometric sequence;  
④ If $a$, $b$, $c$ form a geometric sequence, then $a^2$, $b^2$, $c^2$ also definitely form a geometric sequence.  
Among the above conclusions, the correct serial numbers are __________.

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