
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 the set $X=\{1,2,5,7,11,13,16,17\}$, let $x_{i}$, $x_{j}\in X$. If the equation $x_{i}-x_{j}=k\left(k \gt 0\right)$ has at least three different solutions, write down all possible values of $k$ as ______.

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