
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
Determine the probability that the product of the logarithms of three distinct elements, chosen from the set $\{0.3, 0.5, 3, 4, 5, 6\}$ and denoted as $x, y, z$, is less than zero, i.e., $\lg x \cdot \lg y \cdot \lg z < 0$.

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