<|system|>
Consider the initial value problem
$$
y^{\prime}+\frac{1}{4} y=3+2 \cos 2 t, \quad y(0)=0
$$
Determine the value of $t$ for which the solution first intersects the line $y=12$.</s>.
<|user|>
Can you answer based on context?
<|assistant|>
10.065778