
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
Let  $a_1, a_2, a_3, \dots, a_{20}$  be a permutation of the numbers  $1, 2, \dots, 20$ . How many different values can the expression  $a_1-a_2+a_3-\dots - a_{20}$  have?

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