
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 at various times during the day, the boss gives the secretary a letter to type, each time putting the letter on top of the pile in the secretary's in-box. When there is time, the secretary takes the top letter off the pile and types it. There are 12 letters to be typed during the day, and the boss delivers them in the order $1, 2, 3, ... , 12$. During a coffee break, the secretary tells a colleague that letters $10$ and $12$ have already been typed, but no information about other letters is given. Assume the remaining letters are still in the in-box to be dealt with after the break. The colleague wonders how many such after-coffee typing orders are possible, considering that none of the letters may be left to be typed as one possible scenario.

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