
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 $g(x)$ corresponds to the curve C that is symmetric to the graph of the function $f(x) = 2^x$ about the line $y = x$. Find the range of the function $$y = g\left( \frac {1}{x}\right) \cdot g(4x) \quad \text{for} \quad \frac {1}{8} \leq x \leq 4.$$

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