
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 that the function $f(x)=\frac{2^{x}+b}{2^{x}+1}$ is an odd function defined on the domain $\mathbb{R}$.

(1) Find the analytic expression of the function $f(x)$ and explain its monotonicity.
(2) Solve the inequality $f(2x+1)+f(x)<0$.

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