
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 $f: A \to B$ be a mapping from $A$ to $B$, where $A=B=\{(x, y) \mid x, y \in \mathbb{R}\}$, and $f: (x, y) \to (x-y, x+y)$. Find the element in $A$ that corresponds to the element $(1, 3)$ in $B$.

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