
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 function $f(x) = 4^{x} - 2^{x}$, and real numbers $s$ and $t$ that satisfy $f(s) + f(t) = 0$, let $a = 2^{s} + 2^{t}$ and $b = 2^{s + t}$.

1. Find the range of $f(x)$ when its domain is $[-1, 1]$.
2. Find the functional relationship $b = g(a)$ and the domain of $g(a)$.
3. Find the range of $8^{s} + 8^{t}$.

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