
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
The correct number(s) of the following conclusions is/are $\boxed{\text{answer}}$:

$\quad(1)$ The domains of the functions $y=a^{x} (a > 0 \text{ and } a \neq 1)$ and $y=\log _{a}a^{x} (a > 0 \text{ and } a \neq 1)$ are the same.

$\quad(2)$ The graph of the function $y=k \cdot 3^{x} (k > 0) (k \text{ is a constant})$ can be obtained by translating the graph of the function $y=3^{x}$.

$\quad(3)$ The function $y= \frac {1}{2}+ \frac {1}{2^{x}-1}(x \neq 0)$ is an odd function and the function $y=x \;( \frac {1}{3^{x}-1}+ \frac {1}{2})(x \neq 0)$ is an even function.

$\quad(4)$ If $x_{1}$ is a zero of the function $f(x)$, and $m < x_{1} < n$, then $f(m) \cdot f(n) < 0$.

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