
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 functions $f(x)=\log_{2}(4^{x}+b\cdot2^{x}+4)$ and $g(x)=x$.
(1) Find the domain of $f(x)$ when $b=-5$;
(2) Find the range of $b$ such that $f(x) > g(x)$ is always true.

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