
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
In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $a$, $b$, $c$ form an arithmetic sequence. Among the following conclusions, the correct one(s) is/are: $①b^{2}\geqslant ac$; $② \frac {1}{a}+ \frac {1}{c}\geqslant \frac {2}{b}$; $③b^{2}\leqslant \frac {a^{2}+c^{2}}{2}$; $④B\in(0, \frac {\pi}{3}]$.

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