
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 speed at which sound propagates in the air is referred to as the speed of sound. Some data on the speed of sound and air temperature are shown in the table below:

| Air Temperature $x/^{\circ}\mathrm{C}$ | $0$ | $5$ | $10$ | $15$ | $20$ |
|---------------------------------------|-----|-----|------|------|------|
| Sound Speed $y($m/s$)$                | $331$ | $334$ | $337$ | $340$ | $343$ |

$(1)$ Find the relationship between $y$ and $x$;  
$(2)$ When the air temperature is $24^{\circ}\mathrm{C}$, a person sees fireworks explode and hears the sound 5 seconds later. How far is the person from the fireworks?

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