
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
Evaluate the following expressions for correctness:
(1) $a(x+y) = ax + ay$
(2) $a^{x+y} = a^x \cdot a^y$
(3) $\log (x+y) = \log x + \log y$
(4) $\left(\frac{\log x}{\log a}\right)\left(\frac{\log y}{\log a}\right) = \frac{\log (xy)}{\log a}$
(5) $a(xy) = a^x \cdot a^y$
Which of the following combinations are true?
A) Only 1 and 2 are true
B) Only 1, 2, and 4 are true
C) Only 1, 2, 3, and 4 are true
D) Only 1, 2, and 5 are true
E) Only 1 and 4 are true
A) Only 1 and 2 are true
B) Only 1, 2, and 4 are true
C) Only 1, 2, 3, and 4 are true
D) Only 1, 2, and 5 are true
E) Only 1 and 4 are true

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