
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 $A$ be the set of all points on the Cartesian coordinate plane. If there is a mapping $f: A \to A$ defined as $f: (x, y) \mapsto (x + y, 2x - 3y)$, then find the pre-image of the point $(1, 2)$.

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