
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
A linear stationary dynamic system described by the equation \(3 Y^{\prime}(t) + Y(t) = 4 X^{\prime}(t) + X(t)\) receives a stationary random function \(X(t)\) with a correlation function \(\mathbf{k}_{x}(\tau) = 6 e^{-2|\tau|}\). Find the variance of the random function \(Y(t)\) at the output of the system in the steady-state regime.

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