
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
Find the analytical expressions of $f\left(x\right)$ that satisfy the following conditions:<br/>$(1)$ Given $f\left(x+1\right)=x^{2}-3x+2$, find $f\left(x\right)$;<br/>$(2)$ Given that the function $f\left(x\right)$ is a linear function, if $f\left(f\left(x\right)\right)=4x+8$, find $f\left(x\right)$;<br/>$(3)$ Given $f(\frac{1}{x}+1)=\frac{1}{{x}^{2}}-1$, find $f\left(x\right)$.

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