
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 certain math test consists of 12 multiple-choice questions, each with four options, of which only one is correct. The scoring standard specifies that each correct answer earns 5 points, while no answer or incorrect answer earns 0 points. In this math test, examinee A answered each multiple-choice question according to the rules and could determine that 9 questions were answered correctly. The remaining 3 questions could not determine the correct option. Among these 3 questions, exactly 2 questions could eliminate two incorrect options, while 1 question could only eliminate one incorrect option. When examinee A answered these 3 questions, each question randomly selected an option from the options that could not be eliminated, and the answers to each question did not affect each other. The score obtained by examinee A for selecting questions in this test is denoted as X.

1. Find the probability when X = 55.
2. Find the distribution table and mathematical expectation of X.

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