
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
There are 4 balls in a box, labeled with numbers 1, 1, 2, 3 respectively. Two balls are randomly drawn from the box.  
$(1)$ Find the probability of drawing 2 balls labeled with the number 1.  
$(2)$ Let $X$ be the sum of the numbers on the two drawn balls. Find the probability distribution and the expected value of the random variable $X$.

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