
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 a function $f(x)$, the absolute difference between its roots and the roots of $g(x) = 4^x + 2x - 2$ does not exceed 0.25. Then, $f(x)$ can be one of the following functions. Fill in the correct function number.  
① $f(x) = \frac{4x-3}{x}$ ② $f(x) = (x-1)^2$ ③ $f(x) = e^x - 1$ ④ $f(x) = 4x - 1$.

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