
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
Let $x$, $y$, and $z$ be positive integers such that $x \ge y \ge z$ and they satisfy the equations:
$$x^2 - y^2 - z^2 + xy = 2251$$
$$x^2 + 2y^2 + 2z^2 - 2xy - 3xz - 3yz = -2090.$$
Determine the value of $x$.
A) 250
B) 252
C) 253
D) 255
E) 256

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