
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
The sum of the first $n$ terms of the sequence $\{a_n\}$ is $S_n$. If the terms of the sequence $\{a_n\}$ are arranged as follows: $$\frac {1}{2}, \frac {1}{3}, \frac {2}{3}, \frac {1}{4}, \frac {2}{4}, \frac {3}{4}, \frac {1}{5}, \frac {2}{5}, \frac {3}{5}, \frac {4}{5}, \ldots, \frac {1}{n}, \frac {2}{n}, \ldots, \frac {n-1}{n}, \ldots,$$ the following operations and conclusions are obtained:  
① $a_{23} = \frac {3}{8}$;  
② $S_{11} = \frac {31}{6}$;  
③ The sequence $a_1, a_2+a_3, a_4+a_5+a_6, a_7+a_8+a_9+a_{10}, \ldots$ is a geometric sequence;  
④ The sum of the first $n$ terms $T_n$ of the sequence $a_1, a_2+a_3, a_4+a_5+a_6, a_7+a_8+a_9+a_{10}, \ldots$ is $T_n = \frac {n^2+n}{4}$;  
Fill in the blanks with all the numbers of the operations or conclusions you think are correct \_\_\_\_\_\_.

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