
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 that $f(x)$ is an odd function defined on $\mathbb{R}$, for $x \in [0, +\infty)$, $f(x) = 2^x + x - m$ (where $m$ is a constant).
(1) Determine the value of the constant $m$.
(2) Determine the explicit formula for $f(x)$.
(3) If it holds true that for any $x \in [-3, -2]$, $f(k \cdot 4^x) + f(1 - 2^{x+1}) > 0$, find the range of the real number $k$.

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