
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 random variables \( X = 1, 2, 3, \ldots \) and \( Y = 0, 1, 2 \), with \( P(X=k) = \frac{1}{2k} \), and \( Y \equiv 3 \pmod{X} \), find \( E(Y) \).

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