
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
Supplementary question: The fare structure for a certain type of taxi is as follows: a flat rate of 6 yuan for distances up to 3 kilometers, and beyond 3 kilometers, an additional 1.5 yuan is charged for every extra kilometer (fractions of a kilometer are rounded up to the next kilometer). If a person pays 18 yuan for a taxi ride from location A to location B, and the distance traveled from A to B is $x$ kilometers, formulate an analysis and calculate the maximum value of $x$.

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