
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 lengths of the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, $c$, $c=2$, the area is $S$, and $bcos\frac{A}{2}=S$. Find:<br/>
$(1)$ The measure of angle $A$.<br/>
$(2)$ The range of values for $\frac{{b+c}}{a}$.

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