
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 acute triangle $\triangle ABC$, let the sides opposite angles $A$, $B$, and $C$ be $a$, $b$, and $c$ respectively. It is known that $\sin ^{2}C+\sin ^{2}B-\sin ^{2}A=\sin B\sin C$.<br/>$(1)$ Find the value of angle $A$;<br/>$(2)$ Given that the angle bisector of $A$ intersects $BC$ at point $D$, find the range of values for $\frac{BD}{CD}$.

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