
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
There are two identical pieces of fabric. The total cost of the first piece is 126 rubles more than the cost of the second piece. The cost of four meters of fabric from the first piece exceeds the cost of three meters of fabric from the second piece by 135 rubles. A purchaser bought 3 meters of fabric from the first piece and 4 meters of fabric from the second piece and paid a total of 382.50 rubles. How many meters of fabric were in each of these pieces? What is the cost per meter of fabric from each piece?

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