
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 $r_8(n)$ denote the remainder when $n$ is divided by $8$. What is the $15^\text{th}$ entry in an ordered list of all nonnegative integers $n$ that satisfy 
$$ r_8(7n) \leq 3 $$

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