
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
Tessa picks three real numbers \( x, y, z \) and computes the values of the eight expressions of the form \( \pm x \pm y \pm z \). She notices that the eight values are all distinct, so she writes the expressions down in increasing order. For example, if \( x=2, y=3, z=4 \), then the order she writes them down is
$$
-x-y-z, +x-y-z, -x+y-z, -x-y+z, +x+y-z, +x-y+z, -x+y+z, +x+y+z.
$$

How many possible orders are there?

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