
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 $\triangle ABC$, $a$, $b$, and $c$ are the lengths of the sides opposite to angles $A$, $B$, and $C$ respectively. It is known that $a^{2}-c^{2}=b^{2}-bc$. Find:  
$(1)$ The measure of angle $A$;  
$(2)$ If $a=2$ and $b+c=4$, find the values of $b$ and $c$.

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