
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 $f(x) = 2x + k \cdot 2^{-x}$, where $k \in \mathbb{R}$.

(1) If the function $f(x)$ is an odd function, find the value of the real number $k$;

(2) If for any $x \in [0, +\infty)$, $f(x) > 2 - x$ holds, find the range of values for the real number $k$.

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