
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
A math test consists of 12 multiple-choice questions, each with four options, of which only one is correct. The scoring standard is as follows: 5 points are awarded for each correct answer, and 0 points are awarded for not answering or answering incorrectly. In this math test, student A answered each multiple-choice question according to the rules and could determine the correct answer for 9 questions. The remaining 3 questions had uncertain correct options, with 2 questions being able to eliminate two incorrect options, and 1 question only able to eliminate one incorrect option. When student A answered these 3 questions, they randomly selected an option from the remaining options for each question, and the answers to each question did not affect each other. The score obtained by student A for the multiple-choice questions in this test is denoted as $x$.
1. Find the probability when $x=55$;
2. Find the probability distribution and the expected value of $x$.

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