
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
Given a sample with a capacity of $50$, and the frequency distribution table of its data is as follows:

| Group | $1$ | $2$ | $3$ | $4$ | $5$ |
|-------|-----|-----|-----|-----|-----|
| Frequency | $8$ | $11$ | $10$ | $x$ | $9$ |

Determine the values of $x$ and the ratio of the frequency of the $4$th group to the sample capacity.

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