
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 standards in a certain city are as follows: a fee of $10 is charged for a distance of $3$ kilometers or less (including $3$ kilometers); for distances exceeding $3$ kilometers, the excess distance is charged at a rate of $2.4$ yuan per kilometer (any part less than $1$ kilometer is counted as $1$ kilometer).  
$(1)$ If a taxi travels a distance of $x$ kilometers ($x$ is an integer, and $x \gt 3$), please express the fare to be paid in terms of an algebraic expression involving $x$;  
$(2)$ If a taxi travels a distance of $5.3$ kilometers, how much should be paid for the fare?

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