
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 $f(x)=\frac{4^{x}+a}{2^{x+1}}$, and $h(x)=2f(x)-ax-b$.
(I) Determine the evenness or oddness of $f(x)$ and explain the reason.
(II) If $f(x)$ is an odd function and $h(x)$ has a zero point in $[-1,1]$, find the range of the real number $b$.

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