
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 $a$, $b$, and $c$ be positive integers such that $a \geq b \geq c$ and the following equations hold:
\[ a^2 - b^2 - c^2 + ab = 2500, \]
\[ a^2 + 3b^2 + 3c^2 - 3ab - 2ac - 2bc + b = -2200. \]
What is $a$?
A) 254
B) 255
C) 256
D) 257
E) 258

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