
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]


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A certain online movie platform randomly selected 216 viewers from all the viewers who participated in the evaluation of a recently released film. Some of the data is shown in the table below (unit: people):

|          | Good Review | Bad Review | Total |
|----------|-------------|------------|-------|
| Male     |             | 68         | 108   |
| Female   | 60          |            |       |
| Total    |             |            | 216   |

$(1)$ Please complete the $2\times 2$ contingency table and determine whether there is a $99\%$ certainty that "the evaluation of the film is related to gender."

$(2)$ If we consider frequency as probability, randomly select 3 viewers who gave a "good review" from all the viewers who gave a "good review" on the platform. Let random variable $X$ represent the number of male viewers selected. Find the distribution table of $X$.

$(3)$ Among the 216 people selected, 10 viewers who gave a "good review" were sampled using stratified sampling, and $m$ viewers who gave a "bad review" were sampled. Now, 2 viewers are randomly selected from these $(10+m)$ people. Let random variable $Y$ represent the number of female viewers who gave a "good review" selected. If the expected value of random variable $Y$ is not less than 1, find the maximum value of $m$.

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

Reference data:

| $P(K^{2}\geqslant k_{0})$ | 0.10 | 0.05 | 0.025 | 0.010 | 0.005 | 0.001 |
|---------------------------|------|------|-------|-------|-------|-------|
| $k_{0}$                   | 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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