
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
Merlin has two $100 \times 100$ grids. One grid is blank and hangs on a cliff at the entrance of the cave. The other grid has a number in each cell and hangs on the wall inside the cave. You can specify a square subgrid of any size (from $1 \times 1$ to $100 \times 100$) in the blank grid and pay Merlin a shilling to find out the sum of all the numbers in the corresponding subgrid in the second grid. What is the minimum number of shillings needed to find the sum of all the numbers along the diagonal of the second grid?

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