
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
In a different scenario in an office, there are eleven letters that need to be typed during the day, and the boss delivers them in the order $1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11$. Like before, the boss adds each letter on top of a pile in the secretary's in-box. When there is time, the secretary takes the top letter off the pile and types it. At lunch, the secretary informs a colleague that letter $9$ has already been typed. The colleague, knowing nothing else about the process, wonders about the possible orders in which the remaining letters could be typed after lunch. Assuming that no letter is left untyped by the end of the day, calculate the number of different typing orders possible after lunch.

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