
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 that four different letters $\text{A}$, $\text{B}$, $\text{C}$, and $\text{D}$ are to be placed in a $4 \times 4$ grid, with the letter $\text{B}$ fixed in the upper left corner, calculate the number of valid arrangements.

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