
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 \(r_{11}(7n)\) stand for the remainder left when \(n\) is divided by \(11.\) For example, \(r_{11}(7 \cdot 3) = 10.\)

What is the \(15^{\text{th}}\) entry in an ordered list of all nonnegative integers \(n\) that satisfy $$r_{11}(7n) \leq 5~?$$ (Note that the first entry in this list is \(0\).)

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