
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 a nonnegative integer $n$, let $r_{11}(n)$ stand for the remainder left when $n$ is divided by $11.$ For example, $r_{11}(27)=5.$

What is the $17^{\text{th}}$ entry in an ordered list of all nonnegative integers $n$ that satisfy $$r_{11}(6n)\le 6~?$$ (Note that the first entry in this list is $0$.)

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