
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 the sequence $\{a_n\}$, define $\{\Delta a_n\}$ as the first-order difference sequence of $\{a_n\}$, where $\Delta a_n = a_{n+1} - a_n$ ($n \in \mathbb{N}^*$); generally, define $\{\Delta^k a_n\}$ as the $k$-th order difference sequence of $\{a_n\}$, where $\Delta^k a_n = \Delta^{k-1} a_{n+1} - \Delta^{k-1} a_n$ ($k \in \mathbb{N}^*$, $k \geq 2$). Given that the general term formula of the sequence $\{a_n\}$ is $a_n = n^2 + n$ ($n \in \mathbb{N}^*$), then the correct serial number(s) among the following conclusions is/are __________.  
① $\Delta a_n = 2n + 2$;  
② The sequence $\{\Delta^3 a_n\}$ is both an arithmetic sequence and a geometric sequence;  
③ The sum of the first $n$ terms of the sequence $\{\Delta a_n\}$ is $S_n = n^2 + n$;  
④ The sum of the first 2014 terms of $\{\Delta^2 a_n\}$ is 4028.

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