
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 an office, the boss delivers 10 letters to be typed throughout the day, arranging them on the secretary's in-box  pile in the order $1, 2, ... , 10$. During lunch, the secretary manages to type letters $8$ and $9$ but no other information about typing order is provided. Determine the number of possible orders in which the untyped letters (including possibly the letter 10) can be processed after lunch, considering letter 8 and 9 are already typed. Assume the letters are handled in Last In, First Out (LIFO) manner using a stack.

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