
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 that $f\left(\frac{2}{x}+2\right) = x + 1$, find $f(x)$.
2. Suppose $f(x)$ is a linear function that satisfies $3f(x+1) - 2f(x-1) = 2x + 17$, find $f(x)$.

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