
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 $f(x) = \frac{-2^x + n}{2^{x+1} + m}$ is an odd function defined on $\mathbb{R}$.

(1) Find the values of $n$ and $m$;  
(2) If for any $c \in (-1, 1)$, the inequality $f(4^c - 2^{c+1}) + f(2 \cdot 4^c - k) < 0$ always holds, find the range of the real number $k$.

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