
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
A taxi fare standard in a certain city is as follows: The flag-down fare is $8, and the flag-down distance is $3km$ (if not exceeding $3km$, the fare is charged at the flag-down rate); for distances exceeding $3km$ but not exceeding $8km$, the fare for the excess part is charged at $2.15$ per kilometer; for distances exceeding $8km$, the fare for the excess part is charged at $2.85$ per kilometer. Additionally, a fuel surcharge of $1$ is levied for each ride. Now, if a person paid $22.6$ for a taxi ride, then the taxi traveled a distance of $\_\_\_\_\_\_\_\_(km)$.

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