
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
The graph of the function $f(x)=\sin \left(x- \frac {\pi}{3}\right)$ is denoted as $C$. The following conclusions are drawn:
1. The graph $C$ is symmetric about the line $x= \frac {5\pi}{6}$;
2. The graph $C$ is symmetric about the point $\left( \frac {4\pi}{3},0\right)$;
3. The function $f(x)$ is increasing in the interval $\left[ \frac {\pi}{3}, \frac {5\pi}{6}\right]$.

Among these conclusions, the correct conclusion number(s) is/are ______. (Write down all the correct conclusion numbers)

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