
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
Create a system of two equations with two unknowns \(x\) and \(y\), such that the solutions are only the following three pairs of numbers: \(x=y=1\), \(x=y=2\), and \(x=3, y=4\). In the formulation of the equations, you may use numbers, the variables \(x\) and \(y\), parentheses, the equals sign, standard arithmetic operations, and elementary functions.

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