
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
Find the range of the following functions:
(1) $f(x) = 2^{x+2} - 3 \times 4^x$, where $x \in (-\infty, 1)$;
(2) $f(x) = \log_2{\frac{x}{4}} \times \log_2{2x}$, where $x \in [1, 4]$;
(3) $f(x) = e^{|x|} + |x|$, where $x \in \mathbb{R}$.

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