
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 $ABC$, let the sides opposite to angles $A$, $B$, and $C$ be $a$, $b$, and $c$ respectively. It is given that $2a\cos C + b\cos C + c\cos B = 0$.
(Ⅰ) Find the measure of angle $C$;
(Ⅱ) If $a=2$ and the area of triangle $ABC$ is $\frac{\sqrt{3}}{2}$, find the length of side $c$.

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