
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
Consider a $4 \times 4$ grid where each cell contains a unique integer from $1$ to $16$. The grid must be filled so that the entries in every row, every column, and both main diagonals (from top-left to bottom-right and from top-right to bottom-left) are in strictly increasing order. How many such grids are possible?
**A)** 8
**B)** 16
**C)** 24
**D)** 32

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