
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 \( f: \mathbf{R} \rightarrow \mathbf{R} \) be a continuous monotonic function with \( f(0) = 1 \), which satisfies the inequality
\[ f(x+y) \geq f(x) f(y) - f(xy) + 1. \]

Determine the function \( f(x) \).

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