
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
Find the expected value of the random variable \( Z \) given the expected values of \( X \) and \( Y \):

a) \( Z = X + 2Y \), \( M(X) = 5 \), \( M(Y) = 3 \)

b) \( Z = 3X + 4Y \), \( M(X) = 2 \), \( M(Y) = 6 \)

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