
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
How many orderings \(\left(a_{1}, \ldots, a_{8}\right)\) of \((1, 2, \ldots, 8)\) exist such that \(a_{1} - a_{2} + a_{3} - a_{4} + a_{5} - a_{6} + a_{7} - a_{8} = 0\)?

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