
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 company needs to transport a batch of epidemic prevention materials to a disaster area and plans to rent two types of trucks, $A$ and $B$. When each truck is fully loaded, renting $15$ trucks of type $A$ and $25$ trucks of type $B$ can carry $750$ boxes of epidemic prevention materials; renting $10$ trucks of type $A$ and $30$ trucks of type $B$ can carry $700$ boxes of epidemic prevention materials.<br/>$(1)$ How many boxes of epidemic prevention materials can each truck of type $A$ and type $B$ carry, respectively?<br/>$(2)$ Initially estimated, the company needs to transport no more than $1245$ boxes of epidemic prevention materials. The company plans to rent a total of $70$ trucks of type $A$ and type $B$, with the number of type $B$ trucks not exceeding $3$ times the number of type $A$ trucks. How many different rental plans does the company have to transport this batch of epidemic prevention materials to the disaster area?

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