
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
During a comprehensive practical activity at a school in Wenzhou, students explored the relationship between the number of plants cultivated per pot and the market selling price. Through experiments and market surveys, it was found that when there are $5$ plants or fewer in each pot (including $5$ plants), the quality of the plants is higher, and the selling price per plant is $3$ yuan. After exceeding $5$ plants, for each additional plant per pot, the selling price decreases by $0.3$ yuan. When the number of plants per pot exceeds $12$, the quality of the plants is lower, and the unified purchase price in the market is $0.8$ yuan per plant. Each pot can cultivate up to $18$ plants.<br/>$(1)$ Let each pot cultivate $x$ plants $(5\leqslant x\leqslant 12)$,<br/>① the selling price per plant is ______ yuan, the price per pot is ______ yuan (expressed in algebraic expressions involving $x$);<br/>② when the price per pot is $16.2$ yuan, find the value of $x$.<br/>$(2)$ The student experimental group planted a total of $40$ pots. The cost $y$ (in yuan) required for cultivating each pot is related to the number of plants $x$ (in pots) by $y=2+0.3x$. There are no other expenses for each pot of plants except for cultivation costs. The group gave away $10$ pots to the school and sold the rest in the market. After all were sold, $100$ yuan remained after deducting the cultivation costs. Find the number of plants cultivated per pot.

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