
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
On a $4 \times 4$ board, numbers from 1 to 16 must be placed in the squares, without repetition, so that the sum of the numbers in each row, column, and diagonal is the same. We call this sum the Magic Sum.

a) What is the Magic Sum for this board?

b) If the sum of the squares marked with $X$ on the board below is 34, what is the sum of the squares marked with $Y$?

| $Y$ |  |  | $Y$ |
| :--- | :--- | :--- | :--- |
|  | $X$ | $X$ |  |
|  | $X$ | $X$ |  |
| $Y$ |  |  | $Y$ |

c) If we fill the board with consecutive natural numbers from $k$ to $(k+15)$, so that the Magic Sum is 50, what is the value of $k$?

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