
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
Fruits are divided into first-grade fruits and second-grade fruits, with a total of 136 boxes, including 102 boxes of first-grade fruits and 34 boxes of second-grade fruits.  
$(1)$ Randomly select two boxes of fruits, find the probability of selecting exactly one box of first-grade fruit and one box of second-grade fruit;  
$(2)$ Conduct stratified sampling, selecting a total of 8 boxes of fruits, find the number of boxes of first-grade fruits and second-grade fruits;  
$(3)$ Extract a certain number of boxes of fruits, with a total of 120 first-grade fruits, with an average weight of 303.45 grams and a variance of 603.46; 48 second-grade fruits, with an average weight of 240.41 grams and a variance of 648.21; find the variance and average weight of 168 fruits, and estimate the weight of a single fruit in the orchard.

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