
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 six propositions, the correct ones are __________  
\\(①\\) There exists \\(α\\) such that \\(\sin α + \cos α = \frac{3}{2}\\);

\\(②y = \sin (\frac{5}{2}π - 2x)\\) is an even function;

\\(③x = \frac{π}{8}\\) is a symmetry axis of \\(y = \sin (2x + \frac{5π}{4})\\);

\\(④y = e^{\sin 2x}\\) is an increasing function on \\((0, \frac{π}{2})\\) with a period of \\(π\\);  
\\(⑤\\) If \\(α\\) and \\(β\\) are angles in the first quadrant and \\(α > β\\), then \\(\tan α > \tan β\\);  
\\(⑥\\) The graph of the function \\(y = 3\sin (2x + \frac{π}{3})\\) can be obtained by shifting the graph of \\(y = 3\sin 2x\\) to the left by \\(\frac{π}{3}\\) units.

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