
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
1. Given $f(x+1)=x^{2}+4x+1$, find the expression for $f(x)$.
2. Given $f(x)$ is a linear function, and it satisfies $3f(x+1)-f(x)=2x+9$. Find $f(x)$.
3. Given $f(x)$ satisfies $2f(x)+f\left( \frac{1}{x} \right)=3x$, find $f(x)$.

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