
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
In a certain survey, a stratified random sampling with sample size proportion allocation was used. Some of the data are shown in the table below:

| Sample Category | Sample Size | Mean | Variance |
|-----------------|-------------|------|----------|
| $A$             | $10$        | $3.5$| $2$      |
| $B$             | $30$        | $5.5$| $1$      |

Based on this data, the variance of the total sample is ______.

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