
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 the functions \( f: \mathbb{Q} \rightarrow \mathbb{Q} \) (where \( \mathbb{Q} \) is the set of rational numbers) that satisfy \( f(1)=2 \) and
\[ f(x y) \equiv f(x) f(y) - f(x + y) + 1, \quad \text{for all} \ x, y \in \mathbb{Q}. \]

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