
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
The population is divided into three age groups: $A$, $B$, and $C$, with a ratio of $5:4:1$. A stratified sampling method is used to draw a sample of size $20$ from the population. It is known that the probability of both person $A$ and person $B$ in group $C$ being selected is $\frac{1}{45}$. Calculate the total number of employees in the company.

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