
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
Let the function $f(x) = \frac{b - 2^x}{a + 2^x}$ be defined on the domain $\mathbb{R}$ and be an odd function.

(1) Find the values of $a$ and $b$.
(2) Determine the monotonicity of $f(x)$ on $(-\infty, +\infty)$ (without needing the proof process).
(3) If the inequality $f(t^2 - 2t) > f(-2t^2 + k)$ holds for any $t \in (-1, 3]$, find the range of values for $k$.

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