
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
According to research by psychologists, there is a relationship between students' acceptance ability $y$ of a new concept and the time $x$ (in minutes) spent proposing the concept (where $0\leqslant x\leqslant 30)$ as shown below:

| Time spent proposing concept ($x$) | $2$ | $5$ | $7$ | $10$ | $12$ | $13$ | $14$ | $17$ | $20$ |
|------------------------------------|-----|-----|-----|------|------|------|------|------|------|
| Acceptance ability of concept ($y$)| $47.8$ | $53.5$ | $56.3$ | $59$ | $59.8$ | $59.9$ | $59.8$ | $58.3$ | $55$ |

(1) Which two variables are reflected in the table? Which one is the independent variable and which one is the dependent variable?

(2) Based on the data in the table, at what time spent proposing the concept do students have the strongest acceptance ability?

(3) In what time range do students' acceptance ability of a new concept gradually increase? In what time range do they gradually decrease?

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