
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 the angles $A$, $B$, and $C$ are denoted by $a$, $b$, and $c$ respectively. It is known that $(b - 2a) \cdot \cos C + c \cdot \cos B = 0$.
(1) Find the angle $C$.
(2) If $c=2$ and the area of triangle $ABC$ is represented by $S_{\triangle ABC} = \sqrt{3}$, find the values of the sides $a$ and $b$.

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