
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
Given two sets of data: $x_1, x_2, \ldots, x_n$ and $y_1, y_2, \ldots, y_n$, they have the relationship: $y_i = ax_i + b$ ($i=1, 2, \ldots, n$, where $a, b$ are non-zero constants). If the variances of these two sets of data are $\sigma_x^2$ and $\sigma_y^2$ respectively, then the relationship between $\sigma_x^2$ and $\sigma_y^2$ is.

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