
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 a function $f(x) = \frac{-2^x + n}{2^{x+1} + m}$ with its domain being $\mathbb{R}$ is an odd function.  
① Find the values of $m$ and $n$;  
② If for any $t \in (1, 2)$, the inequality $f(t^2 - 2t) + f(2t^2 - k) < 0$ always holds, find the range of the real number $k$.

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