
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
As an approximate value of the integral \( I = \int_{0}^{\frac{\pi}{2}} \cos x \, \mathrm{d} x \), the estimate \( I_{1}^{*} = (b-a) \frac{\Sigma \varphi(x_{i})}{n} \) is taken. Find the variance \( \sigma^{2} \) of the averaged function \( (b-a) \varphi(X) \).

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