
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 discrete random variable \( X \) given by the probability distribution:

a) \( X = 4, 6, 10 \)

b) \( X = 0.2, 10.5, 40.61 \)

with probabilities:

\( p = 0.2, 0.3, 0.5 \);

\( p = 0.1, 0.5, 0.4 \)

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