
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 \( f: \mathbf{Q} \rightarrow \mathbf{Q} \) that satisfy the conditions \( f(1)=2 \) and the identity

\[ f(xy) \equiv f(x)f(y) - f(x+y) + 1 \quad \text{for} \quad x, y \in \mathbf{Q} \]

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