
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 a monotonically increasing function defined on $\mathbb{R}$ such that for any $x, y \in \mathbb{R}$, $f(x + y) = f(x) + f(y)$.
(1) Determine the parity of the function $f(x)$;
(2) If $f(k \cdot 3^x) + f(3^x - 9^x - 2) < 0$ holds for any $x \in \mathbb{R}$, find the range of values for the real number $k$.

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