
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
Consider the following propositions:
1. There exists a real number $x$ such that $\sin x + \cos x = \frac{3}{2}$.
2. If $\alpha$ and $\beta$ are angles in the first quadrant and $\alpha > \beta$, then $\cos \alpha < \cos \beta$.
3. The function $y = \sin\left( \frac{2}{3}x + \frac{\pi}{2} \right)$ is an even function.
4. Let A, B, C be the acute angles of the triangle ABC, then $\sin A > \cos B$.
Identify the correct propositions by their number.

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