
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
There are $8$ people numbered $1$, $2$, $3$, $\ldots$, $8$ in a line. If we take out the people numbered $6$, $7$, $8$ and insert them in the front of the line, with person $5$ becoming the last one, and the relative order of the original positions of people $1$, $2$, $3$, $4$, $5$ remaining unchanged, calculate the number of different ways to arrange them.

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