
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 $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively, satisfying the equation $(2a-c)\cos B=b\cos C$.
1. Determine the measure of angle $B$.
2. Let $\vec{m}=(\sin A, 1)$ and $\vec{n}=(-1, 1)$, find the minimum value of the dot product $\vec{m}\cdot\vec{n}$.

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