
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 curve $y=(1-x)x^{n}$ ($n∈\mathbb{N}^{*}$), the tangent line $l$ at $x=\frac{1}{2}$ has a y-intercept of $b_{n}$. Find the general formula for the sequence ${b_{n}}$.

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