
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
Let \( f(x) \) be a function defined on \( \mathbf{R}_{+} \) by
\[ 
f(x)=\begin{cases} 
\left|\log_{3}x - 1\right|, & 0 < x \leqslant 9; \\
4 - \sqrt{x}, & x > 9. 
\end{cases}
\]

Given that \( a, b, c \) are three distinct real numbers satisfying \( f(a) = f(b) = f(c) \), find the range of the product \( abc \).

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