
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
If the two roots of the equation $(\lg x)^2 + (\lg 2 + \lg 3) \lg x + \lg 2 \cdot \lg 3 = 0$ are denoted as $x_1$ and $x_2$, find the value of $x_1 \cdot x_2$.

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