
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 has two production lines, $A$ and $B$, processing the same raw materials. In one day, production line $A$ processes $a$ tons of raw materials in $(4a+1)$ hours, while production line $B$ processes $b$ tons of raw materials in $(2b+3)$ hours. On the first day, the company allocated 5 tons of raw materials to production lines $A$ and $B$, both of which completed the processing within the same amount of time. The ratio of tons allocated to production line $A$ to tons allocated to production line $B$ is _____. Before starting work on the second day, the company allocated 5 tons of raw materials based on the results of the first day's allocation, and then allocated $m$ tons of raw materials to production line $A$ and $n$ tons of raw materials to production line $B$. If both production lines can process all allocated raw materials within one day and the processing time is the same, the value of $\frac{m}{n}$ is _____.

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