
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
(1) Let $f(x) = 2^x$ and $g(x) = 4^x$. Given that $g[g(x)] > g[f(x)] > f[g(x)]$, find the range of values for $x$.

(2) Given that the range of the function $y = 4^x - 3 \cdot 2^x + 3$ is $[1,7]$, determine the maximum range of values for $x$.

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