
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 a positive integer $n$, let $y=x^{n}(1-x)$ be a curve, and let $a_{n}$ be the $y$-coordinate of the point where the tangent line to the curve at $x=2$ intersects the $y$-axis. The formula for the sum of the first $n$ terms of the sequence $\left\{ \frac{{a}\_{n}}{n+1} \right\}$ is _______.

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