
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 which of the following trigonometric statements are true:
(1) $\sin(x+y)=\sin x + \sin y$
(2) $\sin(x-y)=\sin x - \sin y$
(3) $\tan(x+y) = \frac{\tan x + \tan y}{1 - \tan x \tan y}$
(4) $\cos(x+y) = \cos x \cos y - \sin x \sin y$
(5) $\cos(2x) = 2\cos^2 x - 1$
A) Only 1 and 2 are true
B) Only 3 is true
C) 3, 4 and 5 are true
D) 1, 2, and 3 are true
E) All are true

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