
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
Numbers  $1$  to  $22$  are written on a board. A "move" is a procedure of picking two numbers  $a,b$  on the board such that  $b \geq a+2$ , then erasing  $a$  and  $b$  to be replaced with  $a+1$  and  $b-1$ . Determine the maximum possible number of moves that can be done on the board.

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