
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 function $f(x) = A\sin(\omega x + \varphi)$ (where $A > 0$, $\omega > 0$, $0 < \varphi < \pi$) is symmetric about the point $M(\frac{5\pi}{12}, 0)$, and one of the lowest points adjacent to point $M$ is $N(\frac{2\pi}{3}, -3)$. Determine the correct judgment among the following options:

1. The line $x = \frac{\pi}{2}$ is a symmetry axis of the function $f(x)$ graph.
2. The point $(-\frac{\pi}{12}, 0)$ is a symmetry center of the function $f(x)$.
3. The sum of the x-coordinates of all intersection points between the graph of $y = f(x)$ ($-\frac{\pi}{12} \leq x \leq \frac{35\pi}{12}$) and the line $y = 1$ is $7\pi$.

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