
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 $f(x)= \frac{a \cdot 2^{x}+a-2}{2^{x}+1} (a \in R)$
(1) If $f(x)$ is an odd function, find the value of $a$.
(2) If $f(x)$ is defined on $[-4,+\infty)$, and for all real numbers $x$ in the domain of $f(x)$, $f(\cos x+b+ \frac{1}{4})\geqslant f(\sin ^{2}x-b-3)$ always holds, find the range of values for the real number $b$.

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