
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
Pasha is playing a computer game that takes place on an infinite grid. Each cell of the grid contains either a treasure or a natural number. The number represents the distance to the nearest treasure in terms of cells (if the treasure requires $A$ steps vertically and $B$ steps horizontally, the cell contains the number $A+B$). Pasha can reveal the content of one cell per move. The objective of the game is to find at least one treasure.

a) Pasha revealed three consecutive horizontal cells, each containing the number 5. What is the minimum number of additional moves Pasha needs to make to definitely find a treasure?

b) Pasha revealed three cells, each containing a number. Is it possible that this information allows Pasha to guarantee finding a treasure on the next move?

c) Pasha knows that every number on the grid does not exceed a fixed $K \geqslant 3$. Can Pasha guarantee finding a treasure in at most $K+3$ moves?

d) Pasha knows that every number on the grid does not exceed 2023. Will Pasha be able to definitely find a treasure within 20 moves?

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