
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
The 22nd FIFA World Cup will be held in Qatar in 2022. This is the second time the World Cup is held in Asia after the Korea-Japan World Cup, with a gap of 20 years. This World Cup is also the first World Cup held in the winter in the northern hemisphere. Each World Cup has a total of 32 teams participating in 64 matches. The group stage is divided into 8 groups, with 4 teams in each group playing a round-robin format totaling 48 matches. The top 16 teams advance based on points, and the subsequent matches are knockout rounds. The round of 16 has 8 matches, the quarter-finals have 4 matches, the semi-finals have 2 matches, followed by a third-place match and a final. The table below shows the statistics of the round of 32 to round of 16 for five World Cups:

|           | European Teams | American Teams | African Teams | Asian Teams |
|-----------|----------------|----------------|---------------|-------------|
| Round of 32 | 66             | 45             | 25            | 24          |
| Round of 16 | 44             | 25             | 25            | 5           |

$(1)$ Complete the contingency table based on the above table:

|           | Round of 16 | Not Round of 16 | Total |
|-----------|-------------|------------------|-------|
| European Region |             |                  |       |
| Other Regions   |             |                  |       |
| Total           |             |                  |       |

and determine if there is a 95% confidence that a team entering the World Cup round of 16 is related to the European region.

$(2)$ Given that in a certain World Cup, 2 European teams have reached the quarter-finals and faced each other, with the winner advancing to the semi-finals. At this point, fans predict that there will be 3 European teams, 2 American teams, and 1 Asian team in the quarter-finals. These 6 teams will play 3 matches against each other, with the winners taking the remaining three semi-final spots. Find the probability that European teams do not face each other.

Given: ${K^2}=\frac{{n{{({ad-bc})}^2}}}{{({a+b})({c+d})({a+c})({b+d})}}$,

| $P(K^{2}\geqslant k)$ | 0.050 | 0.010 | 0.001 |
|-----------------------|-------|-------|-------|
| $k$                   | 3.841 | 6.635 | 10.828 |

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