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

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