
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 $f(x)=ax^{3}-3x^{2}+x+b$, where $a$, $b\in\mathbb{R}$, $a\neq 0$, and the tangent line of $y=f(x)$ at $x=1$ is $2x+y+1=0$, find the expression for the function $f(x)$.

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