
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 $l_{3}^{*}=(b-a) c\left(n_{1} / n\right)$ for estimating the definite integral $I=\int_{a}^{b} \varphi(x) \mathrm{d} x$, where the integrand function is non-negative and bounded ($0 \leqslant \varphi(x) \leqslant c$), based on the interpretation of the integral as an area.

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