
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, a boss gives the secretary a sequence of letters to type, each placed on top of the pile in the secretary's in-box. The secretary types letters from the top of the pile when time permits. There are twelve letters supposed to be typed during the day, and the boss delivers them in a sequence from $1$ to $12$. Midway through the day, the secretary informs a colleague that letter $10$ has already been typed, without providing further details about which other letters have been typed. Given this information, how many different orders of typing the remaining letters could possibly occur after lunch? Assume that the possibility of no letters left is also valid.

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