
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 $\{c_n\}$, if there exists an arithmetic sequence $\{a_n\}$ with all terms being positive integers and a geometric sequence $\{b_n\}$ with all terms being positive integers such that $c_n = a_n + b_n$, then the sequence $\{c_n\}$ is called a "DQ sequence". It is known that the sequence $\{e_n\}$ is a "DQ sequence", and its first 5 terms are: 3, 6, 11, 20, 37. Then $e_n = \_\_\_\_\_\_$.

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