
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 similar office scenario, the boss gives the secretary ten letters to type during the day, placed in order $1, 2, 3, ..., 10$ on top of the pile in the secretary's in-box. The secretary types the letters from the top of the pile whenever possible. By midday, the secretary mentions that letters $9$ and $5$ have already been typed. Assuming no other information about the order of typing is known, how many different orders could the remaining letters be typed after lunch? Assume that a scenario where no letters are left to be typed is also a possibility.

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