
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
During the long break at school, a certain class needs to buy two types of jump ropes, $A$ and $B$. It is known that purchasing 10 ropes of type $A$ and 5 ropes of type $B$ costs a total of $175$ yuan, while purchasing 15 ropes of type $A$ and 10 ropes of type $B$ costs a total of $300$ yuan. Find the cost of one rope of type $A$ and one rope of type $B$.

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