
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 express delivery company in Beihai stipulates that the part of the parcel weighing less than $1$ kg is charged at a flat rate, while the part weighing more than $1$ kg is charged per kilogram. Zhang Li sent parcels to Guangzhou and Shanghai, and the charging standards and actual charges are shown in the table below:

Charging Standards:

| Destination | Flat Rate ($/$) | Excess Charge ($/$ per kg) |
|-------------|-----------------|---------------------------|
| Guangzhou   | $x$             | $y$                       |
| Shanghai    | $x+2$           | $y+3$                     |

Actual Charges:

| Destination | Weight (kg) | Cost ($/$) |
|-------------|-------------|------------|
| Guangzhou   | $3$         | $10$       |
| Shanghai    | $4$         | $23$       |

$(1)$ Find the values of $x$ and $y$;  
$(2)$ Li Le sent $5$ kg of Beihai specialty products to a friend in Guangzhou. How much does he need to pay?

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