
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
Among the following four statements:
\\(①\\) The function \\(y=\cos\left(\frac{2}{3}x+\frac{7\pi}{2}\right)\\) is an odd function.
\\(②\\) Let \\(p\\) and \\(q\\) be simple propositions. If the proposition "\\(p \vee q\\)" is false, then the proposition "\\(\neg p \wedge \neg q\\)" is true.
\\(③\\) By shifting all points on the graph of the function \\(y=\sin(-2x) \left(x \in \mathbb{R}\right)\\) to the right by \\(\frac{\pi}{8}\\) units, we can obtain the graph of the function \\(y=\sin\left(-2x+\frac{\pi}{4}\right) \left(x \in \mathbb{R}\right)\\). The correct statement numbers are __________.

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