
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 $\vartriangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $\sqrt{3}a\cos C=(2b-\sqrt{3}c)\cos A$.

1. Find the measure of angle $A$.
2. Find the range of values for $\cos \left( \frac{5\pi }{2}-B \right)-2\sin^{2}\frac{C}{2}$.

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