
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
Which of the following statements are correct?

1. The interval of decrease for the function $y=\sin\left(2x+\frac{\pi}{3}\right)$ is $\left[k\pi+\frac{\pi}{12}, k\pi+\frac{7\pi}{12}\right], k\in\mathbb{Z}$.
2. A symmetry center of the graph of the function $y=\sqrt{3}\cos 2x - \sin 2x$ is $\left(\frac{\pi}{6}, 0\right)$.
3. Given vectors $\overrightarrow{a}=(1,2)$ and $\overrightarrow{b}=(1,1)$, the projection of $\overrightarrow{a}$ onto $\overrightarrow{b}$ is $\frac{3\sqrt{2}}{2}$.
4. If the equation $y=\sin\left(2x+\frac{\pi}{3}\right)-a=0$ has two distinct real solutions $x_1, x_2$ in the interval $\left[0, \frac{\pi}{2}\right]$, then $x_1 + x_2 = \frac{\pi}{6}$.

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