
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
Derive the formula \( I_{2}^{*}=\frac{1}{n} \sum_{i=1}^{n} \frac{\varphi\left(x_{i}\right)}{f\left(x_{i}\right)} \) for estimating the definite integral \( I=\int_{a}^{b} \varphi(x) \, \mathrm{d} x \), where \( f(x) \) is the density of an auxiliary random variable \( X \) in the integration interval \( (a, b) \); \( x_{i} \) are possible values of \( X \) drawn according to the known density \( f(x) \); and \( n \) is the number of trials.

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