
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 certain commercial area parking lot in Xuzhou operates for 24 hours. The maximum charge for small cars within 24 hours is 60 yuan. The charging method is as shown in the table below:

| Time Period | Charge for within 2 hours (including 2 hours) | Charge after 2 hours |
|-------------|-----------------------------------------------|----------------------|
| 7:30-19:30  | 2 yuan per half hour                        | 3 yuan per half hour, maximum not exceeding 45 yuan per time per parking space |
| 19:30-next day 7:30 | 1 yuan per half hour | 1 yuan per half hour, maximum not exceeding 15 yuan per time per parking space |
|             | If less than half an hour, charge by half hour; for parking across time periods, accumulate charges according to the above standards. |

Xiao Li drives a small car to the commercial area and needs to park the car in the parking lot.

$(1)$ If parked for 2 hours, the parking fee should be ______ yuan;

$(2)$ If parked between 7:30-19:30 for 4.2 hours, calculate how much the parking fee should be;

$(3)$ Xiao Li entered the parking lot at 10:30, parked for x hours, where x is an integer. If Xiao Li leaves between 19:30 and 24:00 on the same day, how much is the parking fee for this parking?

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