
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 $\triangle ABC$, if $8\sin^2 \left(\frac{B+C}{2}\right) - 2\cos 2A = 7$.

(1) Find the size of angle $A$;  
(2) If $a= \sqrt{3}$ and $b+c=3$, find the values of $b$ and $c$.

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