
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 $\triangle ABC$, the sides opposite to $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, and $2R-a=\frac{a({b}^{2}+{c}^{2}-{a}^{2})}{{a}^{2}+{c}^{2}-{b}^{2}$, where $R$ is the radius of the circumcircle of the triangle, and $A$ is not a right angle.<br/>$(1)$ If $B=\frac{π}{6}$, find the value of $A$;<br/>$(2)$ Find the minimum value of $\frac{2{a}^{2}-{c}^{2}}{{b}^{2}}$.

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