
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
The 2022 Winter Olympics will be held in Beijing, where the Winter Olympics mascot "Bing Dwen Dwen" is beloved by many. A situation of "one Dwen Dwen hard to find" has appeared in many places. A souvenir shop provided 150 "Bing Dwen Dwen" on the first day of sales and quickly sold out. The shop decided that customers who did not purchase on the first day could make a reservation to purchase the next day, and starting from the second day, they would supply an additional $m$ items each day $(m$ is a positive integer). After 15 consecutive days of sales statistics, partial data on the supply $y_{1}$ (in units: items) and demand $y_{2}$ (in units: items) on the $x$-th day $(1\leqslant x\leqslant 15$, and $x$ is a positive integer) are shown in the table below. The demand $y_{2}$ is related to $x$ by a quadratic function. (Assume that customers who made reservations on a certain day will purchase on the next day, and the demand on that day does not include the reservations from the previous day.)

| Day $x$ | 1 | 2 | ... | 6 | ... | 11 | ... | 15 |
|---------|---|---|-----|---|-----|----|-----|----|
| Supply $y_{1}$ (items) | 150 | $150+m$ | ... | $150+5m$ | ... | $150+10m$ | ... | $150+14m$ |
| Demand $y_{2}$ (items) | 220 | 229 | ... | 245 | ... | 220 | ... | 164 |

1. Write down the direct functional relationships of $y_{1}$ with $x$ and $y_{2}$ with $x$ (no need to specify the range of $x$).
2. Given that starting from the 10th day, customers with demand do not need to make reservations to purchase (i.e., the total demand in the first 9 days exceeds the total supply, and the total demand in the first 10 days does not exceed the total supply), find the value of $m$. (Reference data: the total demand in the first 9 days is 2136 items).
3. Under the condition of the minimum value of $m$ in question 2, if the price of each "Bing Dwen Dwen" is $100, calculate the sales revenue on the 4th and 12th days.

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