
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 a set of data $x_1, x_2, x_3, x_4, x_5$ with a variance of 2, and another set of data $ax_1, ax_2, ax_3, ax_4, ax_5$ (where $a > 0$) with a standard deviation of $2\sqrt{2}$, find the value of $a$.

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