
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
A certain flower shop purchases $16$ stems of a certain type of flower every day, and then sells them. If the flowers are not sold on the same day, the remaining flowers of that type are discarded. The flower shop recorded the daily demand for this type of flower for $10$ days as follows:<br/>

| Daily Demand $n$ | $13$ | $14$ | $15$ | $16$ | $17$ | $18$ |
|------------------|------|------|------|------|------|------|
| Number of Days   | $1$  | $1$  | $2$  | $4$  | $1$  | $1$  |

$(1)$ Find the number of days in these $10$ days when the flower shop had to discard the flowers of this type;<br/>
$(2)$ When $n < 16$, the daily profit $y$ (unit: yuan) as a function of $n$ is expressed as $y = 10n - 80$; when $n \geq 16$, the daily profit is $80$ yuan.<br/>
① When $n = 14$, what is the profit of the flower shop on that day?<br/>
② Find the frequency of the daily demand for which the daily profit of the flower shop is $70$ yuan in these $10$ days.

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