
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 ≠ 1) defined on the domain R as an odd function.
1. If f(1) > 0, find the solution set of the inequality f(x^2 + 2x) + f(x - 4) > 0.
2. If f(1) = 3/2, and g(x) = a^(2x) + a^(-2x) - 4f(x), find the minimum value of g(x) on the interval [1, +∞) and the value of x when this minimum value is attained.

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