
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 scenario, a boss gives ten letters labeled from 1 to 10 to the secretary throughout the day, stacking each on top of the previous in the secretary's in-box. The secretary types the letters from the top of the pile whenever possible. By midday, the secretary has confirmed that letter 9 has been typed. Determine how many different orders of typing are possible for the remaining letters after lunch.

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