
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 $f(x)$ be an odd function defined on $\mathbb{R}$, and for any $a, b \in \mathbb{R}$, when $a + b \neq 0$, we have $\frac{f(a) + f(b)}{a + b} > 0$.
(1) Compare the relationship between $f(a)$ and $f(b)$ when $a > b$.
(2) If $f(9^x - 2 \cdot 3^x) + f(2 \cdot 9^x - k) > 0$ holds for any $x \in [0, +\infty)$, find the range of real number $k$.

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