
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 $f(x) = a^x - (k-1)a^{-x}$ ($a>0$ and $a \neq 1$) be an odd function defined on the domain $\mathbb{R}$.  
(1) Find the value of $k$;  
(2) If $f(1) < 0$, determine the monotonicity of $B$ and find the range of values of $t$ for which the inequality $f(x^2+tx) + f(4-x) < 0$ always holds;  
(3) If $f(1) = \frac{3}{2}$, and $g(x) = a^{2x} + a^{-2x} - mf(x)$ has a minimum value of $\frac{5}{4}$ on $[1, +\infty)$, find the value of $m$.

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