
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
As the physical education exam is approaching, a certain school conducted a random survey of 50 ninth-grade female students to understand the training situation of the "sit-ups" test. They recorded the number of sit-ups each student could do in one minute and categorized the results into four groups for analysis. The incomplete statistical table is shown below. Based on the information in the table, answer the following questions:

| Group | Number $x$ | Frequency (Number of Students) | Average Number of Sit-ups per Group |
|-------|------------|--------------------------------|-------------------------------------|
| $A$   | $10\leqslant x < 20$ | $n$ | $15$ |
| $B$   | $20\leqslant x < 30$ | $18$ | $26$ |
| $C$   | $30\leqslant x < 40$ | $2n$ | $34$ |
| $D$   | $40\leqslant x\leqslant 50$ | $8$ | $46$ |

$(1)$ If the information in the statistical table is to be represented in a pie chart, the central angle corresponding to group $C$ is ______ degrees.<br/>
$(2)$ The median of the sit-up scores of the 50 female students falls in the ______ group.<br/>
$(3)$ Find the average number of sit-ups for the 50 female students in the survey.<br/>
$(4)$ If in the school's physical education exam, passing the sit-up test requires doing more than 20 sit-ups (including 20), estimate the number of female students out of the 700 ninth-grade students in the school who can pass the physical education exam.

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