
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
If a function $f(x)$ satisfies the condition on domain $D$ that for any $a, b, c \in D$, the lengths $f(a), f(b), f(c)$ can form the sides of a triangle, then $f(x)$ is called a "triangle function on domain $D$." Given that the function $f(x) = kx + 2$ is a "triangle function on the interval $[1, 4]$", the range of real numbers for $k$ is \_\_\_\_\_.

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