
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 that $a > 0$, $a \neq 1$, $x > 0$, $y > 0$, $x > y$, determine the number of correct expressions among the following:
1. $\log_a x \cdot \log_a y = \log_a(x+y)$
2. $\log_a x - \log_a y = \log_a(x-y)$
3. $\log_a\left(\frac{x}{y}\right) = \log_a x \div \log_a y$
4. $\log_a(xy) = \log_a x \cdot \log_a y$

Choices:
A) 0
B) 1
C) 2
D) 3

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