
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 radioactive material decays at different rates based on its isotopes. Isotope A has a half-life of $T_A$ and an initial amount of 100 units, whereas Isotope B has a half-life of $T_B$ and an initial amount of 200 units. If after the same time $t$, the remaining quantity of Isotope A is 50 units, while for Isotope B it is 100 units, find the ratio $T_B/T_A$.
A) $1$
B) $2$
C) $\frac{1}{2}$
D) $\frac{3}{2}$

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