
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 correlation function \(K_{x}\left(t_{1}, t_{3}\right) = \cos \omega t_{1} \cos \omega t_{2}\) of a random function \(X(t)\). Find: 

a) the correlation function; 

b) the variance of the integral \(Y(t) = \int_{0}^{1} X(s) \mathrm{d} s\).

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