
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
In a certain chemical reaction, substance $B$ decomposes into two substances $X$ and $Y$, with the rate of formation of each being proportional to the current amount $b$ of substance $B$. Find the laws governing the changes in amounts $x$ and $y$ of substances $X$ and $Y$ over time $t$, given that at the beginning of the process $b = b_{0}, x = 0, y = 0$, and after one hour $b = \frac{1}{2} b_{0}, x = \frac{b_{0}}{8}, y = \frac{3 b_{0}}{8}$.

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