
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 widespread application of modern Internet technology has spurred the rapid development of the express delivery industry. Xiao Ming plans to send some items to a friend through express delivery and has found that two express delivery companies, Company A and Company B, are suitable options. Company A states that for items weighing no more than $1$ kilogram, the charge is $22$ yuan per kilogram; for weights exceeding $1$ kilogram, the excess weight is charged at $15$ yuan per kilogram. Company B states that the charge is $16$ yuan per kilogram, with an additional packaging fee of $3$ yuan. Let $x$ represent the weight of the items to be delivered by Xiao Ming.<br/>$(1)$ Please write down the functional relationship between the cost $y$ (in yuan) of delivering the items by Company A and Company B, and the weight $x$ (in kilograms);<br/>$(2)$ For what value of $x$ does Xiao Ming save more money by choosing Company B for delivery?

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