
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
In a box, there are 10 balls of the same size, among which 3 are labeled with 1, 4 are labeled with 2, and 3 are labeled with 5. First, a ball is randomly drawn from the box and then put back. After that, another ball is randomly drawn (assuming the probability of drawing each ball is the same). Let the sum of the labels of the balls drawn in the first and second draws be $\epsilon$. Find the distribution and the expected value $E\epsilon$ of the random variable $\epsilon$.

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