
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 prevent the outbreak of the $H_{1}N_{1}$ virus, a biotechnology company has developed a new influenza vaccine. In order to test the effectiveness of the vaccine (if the probability of the vaccine being effective is less than $90\%$, the test is considered unsuccessful), the company selected $2000$ influenza samples and divided them into three groups for testing, with the following results:

| Group | $A$ Group | $B$ Group | $C$ Group |
|-------|-----------|-----------|-----------|
| Vaccine Effective | $673$ | $a$ | $b$ |
| Vaccine Ineffective | $77$ | $90$ | $c$ |

It is known that when one sample is randomly selected from all samples, the probability of selecting a sample from Group $B$ with an effective vaccine is $0.33$.

(I) Using stratified sampling, $360$ samples are selected from all samples. How many samples should be selected from Group $C$?

(II) Given $b\geqslant 465$ and $c\geqslant 30$, find the probability of passing the test.

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