
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 $f(x) = ka^x - a^{-x}$ ($a > 0$ and $a \neq 1$) be an odd function.  
(1) Find the value of the constant $k$;  
(2) If $0 < a < 1$, and $f(x+2) + f(3-2x) > 0$, find the range of $x$;  
(3) If $f(1) = \frac{8}{3}$, and the function $g(x) = a^{2x} + a^{-2x} - 2mf(x)$ has a minimum value of $-2$ on $[1, +\infty)$, find the value of $m$.

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