
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
To reduce the academic burden on students, the "double reduction" policy has been implemented in compulsory education schools nationwide starting from the autumn of 2021. To understand the parents' awareness of the "double reduction" policy, a school conducted a questionnaire evaluation with some parents, randomly selecting 20 questionnaires and recording the scores (scores denoted by $x$, unit: points):  
【Data Collection】  
$88\ \ 81\ \ 96\ \ 86\ \ 97\ \ 95\ \ 90\ \ 100\ \ 87\ \ 80$  
$85\ \ 86\ \ 82\ \ 90\ \ 90\ \ 100\ \ 100\ \ 94\ \ 93\ \ 100$  
【Data Organization】  
| $80\leqslant x \lt 85$ | $85\leqslant x \lt 90$ | $90\leqslant x \lt 95$ | $95\leqslant x \lt 100$ |
|-----------------------|-----------------------|-----------------------|-----------------------|
| 3                     | 5                     | $a$                   | 7                     |

【Data Analysis】  
| Average Score | Median | Mode |
|---------------|--------|------|
| $91$          | $b$    | $c$  |

Based on the information above, answer the following questions:  
$(1)$ Fill in the blanks: $a=$______, $b=$______, $c=______.$  
$(2)$ If this set of data is represented by a pie chart, the central angle of the sector corresponding to the range $90\leqslant x \lt 95$ is ______ degrees;  
$(3)$ 1400 parents participated in this questionnaire evaluation activity. Estimate the number of people with scores not less than $90$ among the 1400 parents through sampling analysis.

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