
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 examine the effectiveness of a certain influenza vaccine, a laboratory randomly selected 100 healthy mice for an experiment and obtained the following contingency table:

|          | Infection | Not Infected |
|----------|-----------|--------------|
| Injected | 10        | 40           |
| Not Injected | 20    | 30           |

Given $P(K^{2}\geqslant k_{0})$:

| $k_{0}$ | 3.841 | 5.024 | 6.635 |
|---------|-------|-------|-------|
| $P(K^{2}\geqslant k_{0})$ | 0.05 | 0.025 | 0.010 |

Under the condition that the probability of making an error does not exceed ______, it can be considered that "vaccination" is related to "influenza infection." Reference formula: ${K}^{2}=\frac{n(ad-bc)^{2}}{(a+b)(c+d)(a+c)(b+d)}$.

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