
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 design studio, a director gives concept sketches to a designer to finalize, each time placing the new sketch on top of a stack in the designer's work area. Throughout the day, the designer organizes ten sketches, given in the order $2, 4, 1, 3, 5, 7, 6, 10, 9, 8$. The director asks that sketches $8$ and $4$ are finalized by the end of the workday and they are indeed completed. After lunch, the designer must continue to finalize any remaining sketches in the correct order based on the stack's current top sketch first.

The director wants to understand how many possible orders remain for the unfinished sketches to be finalized after lunch, acknowledging that having no sketches left (all are completed before lunch) is also a possibility.

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