
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
To further enrich campus activities, the school is preparing to purchase a batch of soccer balls and basketballs. It is known that the cost of buying $7$ soccer balls and $5$ basketballs is the same. The total cost of buying $40$ soccer balls and $20$ basketballs is $3400$ yuan.<br/>$(1)$ Find the cost of each soccer ball and basketball.<br/>$(2)$ If the school plans to purchase a total of $100$ soccer balls and basketballs, with a total cost not exceeding $6300$ yuan, how many basketballs can be purchased at most?

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