
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
For the function $f(x)$ with domain $D$, if there exists $x_0 \in D$ such that $f(x_0) = x_0$, then the point $(x_0, x_0)$ is called a fixed point on the graph of $f(x)$. Given this, if the absolute difference between the zeros of the function $f(x) = 4^x + 2x - 2$ does not exceed $0.25$, then the functions $g(x)$ that satisfy the condition are \_\_\_\_\_\_.  
① $g(x) = 4x - 1$; ② $g(x) = (x - \frac{1}{2})^2$; ③ $g(x) = e^x - 1$; ④ $g(x) = \ln(\frac{\pi}{x} - 3)$.

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