
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
Find all functions \( f: \mathbf{Q} \rightarrow \mathbf{Q} \) (where \( \mathbf{Q} \) is the set of rational numbers) such that:
1. \( f(1) = 2 \)
2. For any \( x, y \in \mathbf{Q} \),
\[ f(xy) = f(x) f(y) - f(x + y) + 1 \]

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