
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 the following propositions:
- \\(①\\) There exists a real number \\(x\\) such that \\(\sin x + \cos x = \frac{3}{2}\\).
- \\(②\\) The function \\(y = \frac{\sin^2 x - \sin x}{\sin x - 1}\\) is an odd function.
- \\(③\\) The function \\(y = |\sin x - \frac{1}{2}|\\) has a period of \\(\pi\\).
- \\(④\\) The sum of the x-coordinates of all intersection points of the graph of \\(y = \ln |x - 1|\\) and the graph of \\(y = -2\cos(\pi x)\\) for \\(-2 \leq x \leq 4\\) is equal to 6.

Fill in the correct proposition numbers \_\_\_\_\_\_ (Fill in all correct proposition numbers).

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