
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
Fill in the nine algebraic expressions into the squares of the grid, so that the sum of the three algebraic expressions in each row, each column, and both diagonals of the grid are equal. Given some of the algebraic expressions in the grid as shown in the table below, find $M-N$ ($M$ and $N$ are algebraic expressions containing $x$).

|  $M$  |        | $x^{2}-x-1$ |
|-------|--------|-------------|
|       |        | $x$         |
| $x^{2}-x$ | $x-1$ | $N$         |

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