
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
If the range of the function $f(x)$ on $[m, n] (m < n)$ is exactly $[m, n]$, then $f(x)$ is called an "equal value mapping interval" of the function. Among the following functions: $① y = x^2 - 1$; $② y = 2 + \log_2 x$; $③ y = 2^x - 1$; $④ y = \frac{1}{x - 1}$. The number of functions that have a unique "equal value mapping interval" is $\_\_\_\_\_\_$.

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