
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
One of Michael's responsibilities in organizing the family vacation is to call around and find room rates for hotels along the root the Kubik family plans to drive.  While calling hotels near the Grand Canyon, a phone number catches Michael's eye.  Michael notices that the first four digits of  $987-1234$  descend  $(9-8-7-1)$  and that the last four ascend in order  $(1-2-3-4)$ .  This fact along with the fact that the digits are split into consecutive groups makes that number easier to remember.

Looking back at the list of numbers that Michael called already, he notices that several of the phone numbers have the same property: their first four digits are in descending order while the last four are in ascending order.  Suddenly, Michael realizes that he can remember all those numbers without looking back at his list of hotel phone numbers.  "Wow," he thinks, "that's good marketing strategy."

Michael then wonders to himself how many businesses in a single area code could have such phone numbers.  How many  $7$ -digit telephone numbers are there such that all seven digits are distinct, the first four digits are in descending order, and the last four digits are in ascending order?

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