
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
For any real numbers $a$, $b$, $c$, $d$, the operation "$\triangle$" between ordered pairs of real numbers $\left(a,b\right)$ and $\left(c,d\right)$ is defined as: $\left(a,b\right)\triangle \left(c,d\right)=\left(ac+bd,ad+bc\right)$. If for any real numbers $u$, $v$, it holds that $\left(u,v\right)\triangle \left(x,y\right)=\left(u,v\right)$, then find the values of $x$ and $y$.

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