
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
Is it possible to omit one number from the sequence $1, 2, \ldots, 2008$ so that the remaining 2007 numbers can be arranged in an order $a_{1}, a_{2}, \ldots, a_{2007}$ such that the differences $\left|a_{1} - a_{2}\right|, \left|a_{2} - a_{3}\right|, \ldots, \left|a_{2006} - a_{2007}\right|, \left|a_{2007} - a_{1}\right|$ are all distinct?

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