
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 famous Song Dynasty mathematician Yang Hui was skilled at transforming continuous quantity problems of finding the area and volume of known geometric shapes into discrete quantity problems. In his book "Detailed Explanation of the Nine Chapters Algorithm $\cdot$ Shanggong," he presented the well-known triangular stack formula $1+\left(1+2\right)+\left(1+2+3\right)+\ldots +\left(1+2+3+\ldots +n\right)=\frac{1}{6}n({n+1})({n+2})$. Given this, the sum of the first $n$ terms of the sequence $\{n^{2}+2^{n}\}$ is ______.

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