
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 movie "China's Ping Pong: The Counterattack" tells the story of the Chinese men's ping pong team's counterattack and return to the peak at the Tianjin World Table Tennis Championships in 1995. The film pays tribute to the national sport, relives historical moments, and portrays self-love and patriotism. In order to understand the audience's feelings about the film, a certain movie platform randomly selected 200 male and 200 female viewers for a survey. Among the 200 male viewers, 120 gave a "thumbs up" rating, and among the 200 female viewers, 90 gave a "thumbs up" rating. 

$(1)$ Complete the following $2\times 2$ contingency table and determine whether there is a $99.5\%$ certainty that the evaluation of the film is related to gender:

| Gender | Evaluation Result | Total |
|--------|-------------------|-------|
| Male   | 120               |       |
| Female | 90                |       |
| Total  |                   |       |

$(2)$ From the randomly selected 400 people, all viewers who gave a "thumbs up" rating were further sampled using stratified sampling by gender to select 7 people to participate in a promotional event. To facilitate the event, 2 people are randomly selected from the 7 people as group leaders. Find the probability that the selected 2 people are of different genders.

Reference formula: ${χ^2}=\frac{{n{{(ad-bc)}^2}}}{{({a+b})({c+d})({a+c})({b+d})}}$, where $n=a+b+c+d$.

Reference data:

| $\alpha $ | $0.10$ | $0.05$ | $0.025$ | $0.010$ | $0.005$ | $0.001$ |
|-----------|--------|--------|---------|---------|---------|---------|
| $x_{0}$   | $2.706$| $3.841$| $5.024$ | $6.635$ | $7.879$ | $10.828$|

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