
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 $p\%$ percentile of a set of numbers ($p\in 0,100$) refers to a value that satisfies the following conditions: at least $p\%$ of the data is not greater than this value, and at least $\left(100-p\right)\%$ of the data is not less than this value. Intuitively, the $p\%$ percentile of a set of numbers refers to the value at the $p\%$ position when the numbers are arranged in ascending order. For example, the median is a $50\%$ percentile. In March 2023, in order to create a civilized city, Hohhot city randomly selected $10$ residents from a certain community to investigate their satisfaction with their current living conditions. The satisfaction index number ranges from $1$ to $10$, with $10$ indicating the highest satisfaction. The satisfaction index numbers of these $10$ residents are $8$, $4$, $5$, $6$, $9$, $8$, $9$, $7$, $10$, $10$. What is the $25\%$ percentile of this data set?

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