
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
For the inequality $a^{x} \gt a^{y}$ ($a \gt 0$ and $a\neq 1$), when $a \gt 1$, $x \gt y$, and when $0 \lt a \lt 1$, $x \lt y$. For the inequality ${(\frac{1}{2})}^{kx-1}＜{(\frac{1}{2})}^{5x-2}$, if the solution set contains no positive integer solutions, then the range of $k$ is ____.

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