
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 \( f(x) = \begin{cases} 
|\log_{2} x|, & 0 < x \leq 4, \\
\frac{2}{3} x^{2} - 8x + \frac{70}{3}, & x > 4 
\end{cases} \).

If \( a, b, c, d \) are distinct and satisfy \( f(a) = f(b) = f(c) = f(d) \), then what is the range of values for \( a \cdot b \cdot c \cdot d \)?

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