
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 the function $f(x) = ka^x - a^{-x}$ ($a > 0$ and $a \neq 1$) is an odd function.  
(1) Find the value of the real number $k$.  
(2) If $f(1) > 0$, find the solution set of the inequality $f(x^2 + 2x) + f(x - 4) > 0$.

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