
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
In Xiangshan County, the taxi fare is calculated based on a segmented cumulative method: a fare of 5 yuan is charged for distances within 3 kilometers (including 3 kilometers); for the part exceeding 3 kilometers but not exceeding 10 kilometers, 2 yuan per kilometer is charged; for the part exceeding 10 kilometers, 3 yuan per kilometer is charged. In addition, a fuel surcharge of 1 yuan is added for each ride. Distances less than 1 kilometer are charged as 1 kilometer. If Xiao Ming spent 38 yuan on a taxi ride from school to home, and the distance from Xiao Ming's home to the school is x kilometers, then the range of x is.

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