
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 set $M=\{h(x) | \text{the domain of } h(x) \text{ is } \mathbb{R}, \text{ and for any } x, h(-x)=-h(x)\}$. Let the function $f(x) = \frac{-2^x + a}{2^{x+1} + b}$ ($a, b$ are constants).  
(1) When $a=b=1$, determine whether $f(x) \in M$, and explain the reason;  
(2) If the function $f(x) \in M$, and for any $x$, $f(x) < \sin\theta$ holds, find the range of $\theta$.

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