
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
Given
$$
\left\{\begin{array}{l}
(a-b) \sin \frac{\theta}{2} \cos \frac{\varphi}{2}+(a+b) \cos \frac{\theta}{2} \sin \frac{\varphi}{2}=0(a, b>0) \\
\frac{x}{a} \cos \theta+\frac{y}{b} \sin \theta=1 \\
\frac{x}{a} \cos \varphi+\frac{y}{b} \sin \varphi=1
\end{array}\right.
$$

Eliminate $\theta$ and $\varphi$, and establish an identity among $x, y, a$, and $b$.

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