
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

$$
I_{1}^{\hbar}=(b-a) \frac{\sum_{i=1}^{n} \varphi\left(x_{i}\right)}{n}
$$

where $x_{i}=a+(b-a) r_{i}$, for estimating the definite integral $l=\int_{a}^{b} \varphi(x) \mathrm{d} x$.

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