
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 $ABC$, with sides $a$, $b$, $c$ that are opposite to angles $A$, $B$, $C$ respectively, it is given that $b^2 + c^2 - a^2 = bc$, $\overrightarrow{AB} \cdot \overrightarrow{BC} > 0$, and $a= \frac{\sqrt{3}}{2}$. The range of values for $b+c$ is __________.

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