
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
The following are four propositions:
1. There exists an $x \in (0, 1)$ such that $(\frac{1}{2})^x > \log_{\frac{1}{2}} x$.
2. For all $k \in [0, 8)$, the range of $y = \log_2 (kx^2 + kx + 2)$ is $\mathbb{R}$.
3. The negation of "There exists an $x \in \mathbb{R}$ such that $(\frac{1}{2})^x + 2x \le 5$" is "There does not exist an $x \in \mathbb{R}$ such that $(\frac{1}{2})^x + 2x \le 5$".
4. The negation of "If $x \in (1, 5)$, then $f(x) = x + \frac{1}{x} \ge 2$" is "If $x \in (-\infty, 1] \cup [5, +\infty)$, then $f(x) = x + \frac{1}{x} < 2$".
Identify the sequence numbers of the true propositions. (Please fill in the sequence numbers of all true propositions)

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