
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
A *Beaver-number* is a positive 5 digit integer whose digit sum is divisible by 17. Call a pair of *Beaver-numbers* differing by exactly  $1$  a *Beaver-pair*. The smaller number in a *Beaver-pair* is called an *MIT Beaver*, while the larger number is called a *CIT Beaver*. Find the positive difference between the largest and smallest *CIT Beavers* (over all *Beaver-pairs*).

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