
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
Initially, on the blackboard are written all natural numbers from  $1$  to  $20$ . A move consists of selecting  $2$  numbers  $a<b$  written on the blackboard such that their difference is at least  $2$ , erasing these numbers and writting  $a+1$  and  $b-1$  instead. What is the maximum numbers of moves one can perform?

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