
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
Azar and Carl now play a modified game of tic-tac-toe on a $4$-by-$4$ grid. Azar starts by placing an $X$ in one of the boxes, followed by Carl placing an $O$ in one of the remaining boxes, and they continue this sequence. The game ends either when all boxes are filled or when one of the players has four of their symbols in a row—horizontal, vertical, or diagonal—whichever comes first, in which case that player wins. Assume the players make their moves randomly. Calculate how many ways the board can be arranged if Carl wins the game by placing his fourth $O$.
A) 560
B) 630
C) 700
D) 770

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