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

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