
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 $a+b\ne 0$, we have $\frac{f(a)+f(b)}{a+b} > 0$.

(1) Compare the sizes of $f(a)$ 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 values for the real number $k$.

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