
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 $ABC$, the sides $a$, $b$, and $c$ satisfy the equation $\frac{b+c}{a} = \cos B + \cos C$.

1. Find the value of angle $A$.
2. Find the range of values for the expression $2\cos^2 \frac{B}{2} + 2\sqrt{3}\cos^2 \frac{C}{2}$.

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