
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]


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During the Qingming Festival, a certain school, in order to commemorate the revolutionary martyrs, requires students to participate in the "Qingming Sacrifice to the Martyrs" activity by either visiting the Revolutionary Martyrs Memorial Hall or participating online. Students can only choose one way to participate. It is known that the ratio of the number of students in the three grades of the middle school, Grade 7, Grade 8, and Grade 9, is $4:5:6$. In order to understand the way students participate in the "Qingming Sacrifice to the Martyrs" activity, a stratified sampling method is used for investigation, and the following data is obtained:

| Grade and Participation Method | Grade 7 | Grade 8 | Grade 9 |
|-------------------------------|---------|---------|---------|
| Visit Memorial Hall            | $2a-1$  | $8$     | $10$    |
| Online Participation           | $a$     | $b$     | $2$     |

$(1)$ Find the values of $a$ and $b$;  
$(2)$ From the students surveyed in each grade of the school who chose to participate in the "Qingming Sacrifice to the Martyrs" activity online, randomly select two students. Find the probability that these two students are from the same grade.

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