
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
Consider the positive integer

$$
n=2^{r}-16^{s}
$$

where \( r \) and \( s \) are also positive integers. Find the conditions that \( r \) and \( s \) must satisfy for the remainder of the division of \( n \) by 7 to be 5. Determine the smallest number that meets this condition.

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