
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
Given a triangle $ABC$ with internal angles $A$, $B$, and $C$ opposite to the sides $a$, $b$, and $c$ respectively. If $(2a-c)\cos B=b\cos C$, and the dot product $\vec{AB}\cdot \vec{BC} = -3$,
1. Find the area of $\triangle ABC$;
2. Find the minimum value of side $AC$.

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