
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
At various times during a day, a boss hands out letters to the secretary, placing each letter on top of the in-box pile. The secretary types the letters following the Last In, First Out order. On a particular day, there are ten letters to be typed, numbered $1, 2, 3, \ldots, 10$, handed in this order. The secretary typed several letters before lunch, including letter 8 but hasn't yet typed letter 10. Considering that letter 10 must also be typed after lunch, how many possible orders of typing the remaining letters are there after lunch? Note: The secretary could have received letter 10 before lunch or might receive it after lunch.

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