
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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Apples are common nutritious fruits in people's daily lives. In a certain fruit wholesale market, Fuji apples from 5 different origins are sold, each with the same packaging specifications. The wholesale prices (in yuan per box) and market shares of each origin are as follows:

| Origin | $A$   | $B$   | $C$   | $D$   | $E$   |
|--------|-------|-------|-------|-------|-------|
| Price  | $150$ | $160$ | $140$ | $155$ | $170$ |
| Market Share | $15\%$ | $10\%$ | $25\%$ | $20\%$ | $30\%$ |

Market share is also known as "market share," which refers to the proportion of sales volume of a product in the market among similar products.

(I) Randomly select a box of Fuji apples sold in the wholesale market and find the probability that the price of the apples in the box is less than $160$ yuan.

(II) Conduct stratified sampling according to market share, randomly select $20$ boxes of Fuji apples for inspection,

1. From origins $A$ and $B$, a total of $n$ boxes are selected. Find the value of $n$.
2. Randomly select two boxes from these $n$ boxes for quality inspection. Find the probability that the two boxes are from different origins.

(III) Due to the influence of planting scale and apple quality, it is expected that the market share of origin $A$ will increase by $5\%$ next year, and the market share of origin $C$ will decrease by $5\%$. The market share of other origins remains unchanged, and the apple selling price remains the same (without considering other factors). If the average wholesale price of apples this year is $M_{1}$ per box, and next year it is $M_{2}$ per box, compare the sizes of $M_{1}$ and $M_{2}$. (Only write the conclusion).

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