
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

If at the beginning of the time measurement there was \( m_{0} \) grams of substance \( A \) and \( 2 m_{0} \) grams of substance \( B \), then after any number of \( t \) years, as a result of the radioactive decay of these substances, there will remain \( \boldsymbol{m}=\boldsymbol{m}_{0} \cdot 2^{-\lambda_{1} t} \) and \( M=2 m_{0} \cdot 2^{-\lambda_{2} t} \), where \( \lambda_{1} \) and \( \lambda_{2} \) are constants that depend on the nature of the substances. Calculate the half-life of each of these substances, i.e., find out how many years it will take for half of each substance's initial amount to remain, given that the half-life of substance \( B \) is twice less than that of substance \( A \), and that after 20 years the total mass of these substances decreases 8 times.

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