
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 binary operation $\star$ on ordered pairs of integers be defined by $(a,b)\star (c,d) = (a-c, b+d)$. If $(2,2)\star (4,1)$ and $(x,y)\star (1,4)$ represent identical pairs, find the value of $x$.
A) -1   
B) 0   
C) 1   
D) -2   
E) 2

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