
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 the general term and recursive relation of the following sequences:
① The sequence $\{a_n\}$ ($a_n=n$) has the recursive relation $a_{n+2}=2a_{n+1}-a_n$;
② The sequence $\{b_n\}$ ($b_n=n^2$) has the recursive relation $b_{n+3}=3b_{n+2}-3b_{n+1}+b_n$;
③ The sequence $\{c_n\}$ ($c_n=n^3$) has the recursive relation $c_{n+4}=4c_{n+3}-6c_{n+2}+4c_{n+1}-c_n$;
④ The sequence $\{d_n\}$ ($d_n=n^4$) has the recursive relation $d_{n+5}=5d_{n+4}-10d_{n+3}+10d_{n+2}-5d_{n+1}+d_n$;
Try to guess:
The similar recursive relation of the sequence $\{e_n\}$ ($e_n=n^5$) is \_\_\_\_\_\_.

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