
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
Albrecht writes numbers on the points of the first quadrant with integer coordinates in the following way: If at least one of the coordinates of a point is 0, he writes 0; in all other cases the number written on point  $(a, b)$  is one greater than the average of the numbers written on points  $ (a+1 , b-1) $  and  $ (a-1,b+1)$  . Which numbers could he write on point  $(121, 212)$ ?
Note: The elements of the first quadrant are points where both of the coordinates are non- negative.

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