
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
Define the odd function $f(x) = \frac{b - h(x)}{1 + h(x)}$ with domain $\mathbb{R}$, where $h(x)$ is an exponential function and $h(2) = 4$.
1. Find the analytic expression for the function $f(x)$.
2. Solve the inequality $f(2x - 1) > f(x + 1)$.

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