
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
All the numbers  $1,2,...,9$  are written in the cells of a  $3\times 3$  table (exactly one number in a cell) . Per move it is allowed to choose an arbitrary  $2\times2$  square of the table and either decrease by  $1$  or increase by  $1$  all four numbers of the square. After some number of such moves all numbers of the table become equal to some number  $a$ . Find all possible values of  $a$ .

I.Voronovich	

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