
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 physical examination results of two badminton teams, Team A and Team B, are as follows: the average weight of Team A is $60kg$ with a variance of $100$, and the average weight of Team B is $64kg$ with a variance of $200$. It is also known that the ratio of the number of players in Team A to Team B is $1:3$. Find the variance of all players in Team A and Team B combined.

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