
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
Given that the school's math teaching research group held a math knowledge competition (out of $100$ points) with $1000$ participants from the first grade, $800$ participants from the second grade, and $600$ participants from the third grade, the sample mean scores of the participants from the second and third grades were $76$ and $82$ respectively, and the sample mean score of all participants in the school was $75$. Find the sample mean score of the participants from the first grade.

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