
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
Given the expectation \( m_{x}(t) = 3t^2 + 1 \) of the random function \( X(t) \), find the expectation of the integral \( Y(t) = \int_{0}^t X(s) \, \mathrm{d}s \).

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