
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 conclusions:

1. The function $y=\sin (k\pi -x)$ $(k\in \mathbb{Z})$ is an odd function;

2. The graph of the function $y=\tan (2x+\frac{\pi }{6})$ is symmetric about the point $\left(\frac{\pi }{12},0\right)$;

3. The graph of the function $y=\cos (2x+\frac{\pi }{3})$ has a line of symmetry at $x=-\frac{2}{3}\pi$;

4. If $\tan (\pi -x)=2$, then $\cos^2x=\frac{1}{5}$.

The correct conclusion numbers are __________ (Fill in all the correct conclusion numbers).

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