
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 an acute triangle $ABC$ with sides $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively, and $\tan B + \tan C = \frac{{\sqrt{3}\cos A}}{{\cos B \cos C}}$.  
$(1)$ Find the value of angle $A$.  
$(2)$ If $a = \sqrt{6}$, find the range of values for $b + c$.

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