
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
Given is a  $n\times n$  grid with all squares on one diagonal being forbidden. You are allowed to start from any square, and move one step horizontally, vertically or diagonally. You are not allowed to visit a forbidden square or previously visited square. Your goal is to visit all non forbidden squares. Find, with proof, the minimum number of times you will have to move one step diagonally

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