
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
The entries in a $4 \times 4$ matrix include all the integers from $1$ through $16$. Each row and column must contain numbers in strictly increasing order. Determine the number of such matrices where the numbers 8, 9 are positioned in the two central positions of the $4 \times 4$ grid in any order.
**A) 1200**
**B) 2100**
**C) 2450**
**D) 2800**
**E) 3150**

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