
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 taxi fare in a certain city is as follows: within $3$ kilometers (including $3$ kilometers), the fare is $8$ yuan. For distances exceeding $3$ kilometers, an additional charge of $1.4 yuan per kilometer is applied.<br/>$(1)$ Write down the relationship between the fare $y$ (in yuan) and the travel distance $x$ (in kilometers);<br/>$(2)$ How much does person A need to pay for a $13$-kilometer ride?

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