
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
The set  $M$  consists of all  $7$ -digit positive integer numbers that contain (in decimal notation) each of the digits  $1, 3, 4, 6, 7, 8$  and  $9$  exactly once.
(a) Find the smallest positive difference  $d$  of two numbers from  $M$ .
(b) How many pairs  $(x, y)$  with  $x$  and  $y$  from M are there for which  $x - y = d$ ?

(Gerhard Kirchner)

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