
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
Since 2021, the "Study Strong Country" app has launched a "Four-Person Match" answer module. The rules are as follows: Users need to answer two rounds of questions in the "Four-Person Match". At the beginning of each round, the system will automatically match 3 people to answer questions with the user. At the end of each round, the four participants will be ranked first, second, third, and fourth based on their performance. In the first round, the first place earns 3 points, the second and third places earn 2 points each, and the fourth place earns 1 point. In the second round, the first place earns 2 points, and the rest earn 1 point each. The sum of the scores from the two rounds is the total score of the user in the "Four-Person Match". Assuming that the user has an equal chance of getting first, second, third, or fourth place in the first round; if the user gets first place in the first round, the probability of getting first place in the second round is 1/5, and if the user does not get first place in the first round, the probability of getting first place in the second round is 1/3. 

$(1)$ Let the user's score in the first round be $X$, find the probability distribution of $X$;  
$(2)$ Find the expected value of the user's total score in the "Four-Person Match".

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