
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
(1) The negation of the proposition "For all $x \in \mathbb{R}$, $x^2 + 2x + m \leqslant 0$" is ______.

(2) Given $A = \{ x | x^2 - x \leqslant 0 \}$, $B = \{ x | 2^{1-x} + a \leqslant 0 \}$. If $A \subseteq B$, then the range of the real number $a$ is ______.

(3) Let the function $f(x) = \begin{cases} x + 1, & x \leqslant 0 \\ 2^x, & x > 0 \end{cases}$. Then the range of $x$ that satisfies $f(x) + f(x - \frac{1}{2}) > 1$ is ______.

(4) If $a, b \in \mathbb{R}$, $ab > 0$, then the minimum value of $\frac{a^4 + 4b^4 + 1}{ab}$ is ______.

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