
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 population is divided into three layers $A$, $B$, and $C$, with their individual counts in a ratio of $3:6:1$. Using stratified sampling, a sample of capacity $20$ is drawn from the population. Given that the probability of both elements $a$ and $b$ from layer $C$ being sampled is $\frac{1}{21}$, determine the total number of individuals in the population.

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