
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 city $A$, the taxi fare is calculated as follows: If the trip does not exceed $3$ kilometers, it is charged at the "base fare" of $10$ yuan; if the trip exceeds $3$ kilometers, then the next $2$ kilometers are charged at the "distance fare", which is $1.5$ yuan/kilometer; if the trip exceeds $5$ kilometers, the remaining distance is charged at the "return fare", which is $2.5$ yuan/kilometer. Suppose a person's travel distance is $x$ kilometers, there are two travel plans: $①$ Take one taxi for the entire trip; $②$ Change to a new taxi every $5$ kilometers.
$(Ⅰ)$ Write the pricing functions for the two travel plans;
$(Ⅱ)$ For different travel distances, which of the two plans, $①$ or $②$, is cheaper? Please explain the reason.

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