
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 $4 \times 4$ matrix where each row and each column forms an arithmetic sequence with four terms. The middle squares are labeled $X$ and $Y$ as shown in the matrix, where they form the central $2 \times 2$ submatrix. You are given:
- The first term of the first row is $3$, and the fourth term is $18$.
- The first term of the fourth row is $4$, and the fourth term is $28$.
Determine the value of $X + Y$.
**A)** $\frac{50}{3}$  
**B)** $\frac{94}{3}$  
**C)** $\frac{98}{3}$  
**D)** $\frac{100}{3}$

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