
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]


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Given a function $f(x)$, if there exists a real number $x$ in its domain such that $f(-x) = -f(x)$, then $f(x)$ is called a "restricted odd function".
(1) Determine whether $f(x) = x^2 + 2x - 4$ is a "restricted odd function" and explain why.
(2) If $f(x) = 2^x + m$ is a "restricted odd function" defined on $[-1, 2]$, find the range of values for the real number $m$.
(3) If $f(x) = 4^x - m \cdot 2^{x+1} + m^2 - 3$ is a "restricted odd function" defined on $\mathbb{R}$, find the range of values for the real number $m$.

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