
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
When two distinct digits are randomly chosen in  $N=123456789$  and their places are swapped, one gets a new number  $N'$  (for example, if 2 and 4 are swapped, then  $N'=143256789$ ). The expected value of  $N'$  is equal to  $\frac{m}{n}$ , where  $m$  and  $n$  are relatively prime positive integers. Compute the remainder when  $m+n$  is divided by  $10^6$ .

*Proposed by Yannick Yao*

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