
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 the operation $f(a*b)$ is defined as 
$$
f(a*b) = 
\begin{cases} 
b & \text{if } a \geq b \\
a & \text{if } a < b \\
\end{cases}
$$
determine the range of the function $f(3^x * 3^{-x})$.

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