
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 school randomly selected 20 ninth-grade students to investigate the time they spend on physical exercise each day. The data obtained (in minutes) are as follows: $30, 60, 70, 10, 30, 115, 70, 60, 75, 90, 15, 70, 40, 75, 105, 80, 60, 30, 70, 45$. After analyzing the data, the following Table 1 and Table 2 were obtained:

Table 1

| Time $t$ (minutes) | $0\leqslant t \lt 30$ | $30\leqslant t \lt 60$ | $60\leqslant t \lt 90$ | $90\leqslant t \lt 120$ |
|---------------------|----------------------|-----------------------|-----------------------|------------------------|
| Number of students  | $2$                  | $a$                   | $10$                  | $b$                    |

Table 2

| Mean     | Median  | Mode  |
|----------|---------|-------|
| $60$     | $c$     | $d$   |

Based on the information provided above, answer the following questions:

$(1)$ Fill in the blanks:
① $a=$______, $b=$______;
② $c=$______, $d=$______;

$(2)$ If the school currently has 200 ninth-grade students, estimate the number of students who spend at least the average time on physical exercise each day.

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