
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 $f(x) = \log_{9}(9^{x} + 1) + kx$ ($k \in \mathbb{R}$) is an even function.  
(1) Find the value of $k$;  
(2) Solve the inequality $f(x) - \log_{9}(a + \frac{1}{a}) > 0$ ($a > 0$).

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