
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 function $f(x)$ is defined as follows:
\[f(x)=
\begin{cases}
3^{x-1}-2, & x\in(-\infty,1] \\
3^{1-x}-2, & x\in(1,+\infty) \\
\end{cases}
\]
Determine the range of $f(x)$.

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