
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
By how much is one of the two positive numbers greater than the other if their arithmetic mean is $2 \sqrt{3}$ and their geometric mean is $\sqrt{3}$?

(Hint: The geometric mean of two numbers $m$ and $n$ is defined as $p=\sqrt{\mathrm{mn}}$).

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