
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 the following function $f\left(x\right)$.
1. Given a linear function $f\left(x\right)$ satisfies $f\left(f\left(x\right)\right)=4x-1$, find $f\left(x\right)$.
2. Given $f\left(1-x\right)=2x^{2}-x+1$, find $f\left(x\right)$.

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