
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 function $f(x)=10\sin x+ \frac{1}{6}x^{3}$, the tangent line at $x=0$ is parallel to the line $nx-y=0$. Find the coefficient of $x^{4}$ in the expanded form of the binomial $(1+x+x^{2})(1-x)^{n}$.

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